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International lntercomparison of Neutron . Spectra Evaluating Methods Usüng Activation Detectors

prepared by A. Fischer * November 1974

* on leave from Central Research Institute for Physics Budapest, Hungary

C o n t e n t s

Abstract

Introduction 1

General characterization of the returned spectra 6

Evaluation of the returned spectra 13

- Integrals of the deviation of the spectrum from 14 the ref erence over the neutron energy

- Integral fluxes 18

- Detector activities 19

Discussion and conclusions 23

Literature 25

Appendix (Spectra arranged after the names of 27 the authors)

- Bricka,M., M.Morgues 28

- Buxerolle,M., 43

- Cuculeanu,v., D.Mocioiu 50

- Hrabovcova,A., 66

- Joneja,O.P., D.V.S.Ramakrishna, M.P.Navalkar 69

- Kam,F.B.K., 86

- Martin,G.C., 100

- McElroy,W.N., 105

- Meixner,Ch., 110

- Morin,J., J.Dorlet 126

- Najzer,M., 138

- Nakamura,T., 155

- Sangiust,v., 160

- Turi,L., A.Fischer 165

- Skoda Works 170

- Zijp,W.L., 177

ABSTRACT

The International Intercomparison of Neutron Spectrum Evaluation Methods Using Activation Detectors was organized by the IAEA in 1971 - 1972. All of the oontributions and the results of a critical evaluation are presented here. The apectra of different contributors are compared to a reference spectrum by means of different integrale and weighting functions. Different cross section sets, foil numbers, energy point systems, guess spectra used by the contributors causes differences in the resulting speotra. The posaible ways of separating these effeots are also investigated. Suggestions are made for the organization of a new intercomparison on the basis of more uniform input data.

This work has been made during an IAEA-fellowship in Jülich.

2

this problem certain additional initial physical inf'ormation is required. In the different programmas the additional initial information is taken into account on different. way. The different laboratories dispos~ of different crosa saction sets, and in the different programmes different energy point structures are used. Most of the programmes involve the use o:f threshold detectors only, in some of them the resonance and thermal detectors can be taken int.o account as well.

In the light of thesa developments, the IAEA Working Group on Reactor Radiation Measurement.s at its meatings in March 1970 and April 1971 recommended that the Agency implement a programme for an international intereompfirison o·:f spectrum evaluation methods used recently in the different laboratories of the member states.

The IAEA sent out invitation ta prospactiva participants, who were known to be int.e.rested in this field to take part in the Intarcomparison& Two reaction. rate sets have been sent to the participants of the Intercomparison (Tab& 1„ ) ... These sets wera the only information about the spectra which could be used by the participants. They had t.o use their own programmes, own cross sections„ gue:ss spectra ( if any )~ energy point. systems, etc&

The reaction rate sets have been aupplied by W&N„McElroy of WADCO. They are the measured reactian rates of the activation detectors in the APFA-III ( Godiva ) eore and in the ECELcore 16 mockup of a mixed oxid fueled fa:st breeder reaetor respecti vely.,. Two spectra have bee.n supplied as well by McElroy ( Fig„ 1& end 2., with the 90 % activation energy bo11I1.ds of the used activation detectors )~ these spectra had not been. available to the participants. The two spectra represented the results of SAND-II /17/ calculatians, in which the initial (guess ) spectra have been derived from reactor physics calculations& The result speqtra have been carefully compared with reactor calculations and show good agreement„ These speetra are used by ua aa a reference in the evaluation of the returned resul ts ..

Foil Number Reaction 5Qectrum I (x 1015) 5~ectrum II {x 1015)

1 23Na(n,y)24Na 0.0122 ±7% 0.00261 ±5% 2 24Mg~n,p~24Na 0.0337 ±7% 0.000151 ±3% 3 2 7 A 1 n , a 2 4N a 0.0160 ±2%* 0.0000588 ±3% 4 "Al (n ·r 2 'Mg 0.0945 ±7%* 5 31p~n,p 315; 0.780 ±10% 6 325 n, p 32p 1. 54 ±7%* 0.00658 ±7% 7 455c(n,y) 465c 0.293 ±7% 0.0445 ±5% 8 46Ti~n,p 465c 0.288 ±7% 0.00135 ±6% 9 54 Fe n,p 54Mn 1. 78 ±2%* 0.00909 ±5%

10 55Mn(n,y 56Mn 0.0707 ±10% 11 56Fe(n,p 56Mn 0.0263 ±9%* 0.0000697 ±15% 12 5BFe(n,y)59Fe o. 125 ±7% 0.00962 ±5% 13 5aN; ~n ,pr5sco 2.40 ±2%* 0.0134 ±2% 14 59co n,y 60co 0.255 ±7% o. 105 ±10% 15 63Cu(n,y) 64Cu 0.468 ±7% 0.0793 ±5% 16 6 3cu~n,a) 60 co 0.0000602 ±25% 17 63cu n,2n) 62Cu 0.00256 ±10% 18 115In(n,n•)115m1n 4.74 ±5%* 0.0349 ±5% 19 127I(n,2n~12sr 0.0244 ±7% 0.000122 ±10% 2ü 197Au(n,y 19BAu 4.61 ±7%* 1. 09 ±4% 21 232Th(n,f)F.P. 1. 93 ± 10% 0.0107 ±9% 22 235U(n,f)F.P. 41.9 ±2%* 2.20 ±2% 23 237Np(n,f)F.P. 34.3 ±7% 0.389 ±7% 24 238U(n,f~F.P. 6. 77 ±2%* 0.0493 ±3% 25 23BLJ(n,y 239LJ 3.30 ±5%* 26 239Pu(n,f)F.P. 61. 9 ± 10% 1.59 ±15%

a. DP5/nuclei or fissions/sec-nuclei at a reactor power of 130 watts for 5pectrum I and 162 watts for 5pectrum II. An asterisk indicates an estimated one standard error value for results based on more than one laboratory. Other values are estimated as one standard deviation for an individual laboratory result.

Table 1. The measured reaction rates

1 o-10 10-9 10-8 ro-7 . m-6 10-5 i o-4 10-3 i 0-2 10-1 10° 10 1 1 0 2

10111 1 '

1 1 1 1 1 1 1 1 1 1 1 1011

-> w L .......

10 1~ / '"'

+iolO u w (f)

....... N

* * 10'1 / CU63 ( N2N l CU6'\ D +io

9 L -u 1127( N2N) 1126 ....... MG24(NPJNR24 z RL27(NHEJNR24

FE56(NPJMNS6 z 10

8+ / "J ') ( RL27CNPJMG27 9 +10 8

TI46(NPJSC46

X

V S32(NPJP32

:::l FE54(NPJMNS4

~\ -i-10 7

+: _J P31(NPJSl31 LL 107 NISB(NPJCDSB _J TH232(NfJf,p, c:::==:J er U23BCNFlf.P. c::::==i ...... INllS(NNJINllSM ~ f-z NP237(NFJF.P.

106 1 +10 6 w PU239CNFJf .p. et:: U235(NFJf.p. w FE58(NGJFES9 LL LL U23BCNGJU239 ...... NR23(NGJNR24 0 10 5 CD59(NGJCD60 1 +10

5 SC45(NGJSC46 RU197CNGJRU19B

CU63CNGJCU64

104 1 1 1 1 1 1 1 1

' 1

'

1

' 1 0 4

1 o-10 1 o-9 1 o-s 1 0-1 10-6 10-5 10-4 1 0-3 10-2 10-1 1 0° 101 102

ENERGY IN MEV

FIG. 1. THE REFERENCE 5~ECTRUM GIVEN BY MCELROY ( IAEA-I. l

1 o-10 1 0 -9 1 0 -0 1 0 -7 10-6 1 0 -5 1 0 -4 1 0 -3 10-2 10-1 10° 10 1 10 2

1012 i 1 1 1 1 1 1 1 1 1 1 1 1

1012 ~

> w :L

" 10 1-4- /'\ +io11 (_)

w (j)

" N 10 1~ ~ \ ~ ~ +iolO * ('...._

* :L (_)

V " 127lN2Nll126 0

z 10

9 MG (NPINR24 D +io9

RL27[ c:::::J

z c:::::J ~ c:::J

X 106 c:::::::::J +lÜ 6 =i S32[NPIP32 c:::J U1 _J FES4lNPIMNS4 LL NJSB(NPICDSB _J TH232lNFJF.P.

QJ a: 107 U238(NFJF.P. +io

7 ~ JNl JS( NN 1 !NI !SM f-z NP237lNFJF.P. w NR23(NGINR24 et::

106 SC4SlNGJSC46 \ +io

6 w PU239(NFJF.P. LL LL U23SlNFJf .p. ~ CU63lNGJCU64 D FESBrNGIFES9

105 \ +io

5 MNSS(NGJMNS5

CDS9rNGJCD50 RU197lNGIRU198

10

4

'

1 1 1 1 1 1 1 1 1' 1 104

1 o-10 1 o- 9 10-6 10-7 1 o-6 10-5 10-4 10-3 1 0-2 10-1 10° 101

1 02

ENERGY IN MEV

FIG. 2. THE REFERENCE SPECTRUM GIVEN BY MCELRDY l IRER- 11 . l

6

18 returns have been received0 The returned results, whioh contained more than 30000 numbers altogether, had been

written by the authors only on the line printer and another papar sheets and had to be punched here on cards. By better organisation of the Intercomparison this step and the accom

panying punching errors could be avoided.

A preliminary evaluation of the returns has been accomplished by Hasenclever and presented on the 3rd Meeting of the IAEA Working Group on Reactor Radiation Measurements

in Seattle, 1972 /23/.

The complete evaluation has been accomplished in Jülich in 1973 - 1974. The report presented here contains all of the returned spectra and the details of the evaluation work.

GENERAL CHARACTERISATION OF THE RETURNED SPECTRA

18 authors have sent us their spectra; for the I. Spec

trum 59, for the II* Spectrum 34 results have been reoeived

( Tab. 2 ). The returned speotra are shown in the Appendix.

The results of one of the authors are simply wrong, an other author has sent his results in graphical form only; these spectra could not be taken into account. Only 4 authors have

calculated the spectra in the full energy range in the form of differential spectrum ( 7 - 7 spectra for the Ie and II. Spectrum respectively )e These spectra together with the re

ferences are shown on the Fig. 3 - 6.

3 more authors have oalculated the spectra in the full energy range, but in these sp:ectra the thermaili and the reso

nance regions are represented only by one or two neutron groupse

9 authors have used only threshold deteotors, their re

sul ts contain respectively only the fast regions of the spectrao

A great number of different programmes have been used

by the authors /1-22/. The SAND-II code /17/ has been used by 3,

Author Method Number of Energy range Guess Remarks the spectra in MeV librar'

~

I. II.

BRICKA (France) Linear combination 3 2 10- 8-22.4 No 11-group spectra of model sp. / 1-3/ only

BUXEROLLE (France) Direct inversion 1 1 10- 9-15. No 12- and 13-group

and correction /4/ spectra only

CUCULEANU et al. RDMM /5/ 7 - 0.1-10. No ( Roum.) Orthoßonal polynom 5 0.1-10. No method /6-8/ -

Taylor series /9-10/ 2 - 0.1-10. No HRABOVCOVA (Czech. RDMM /5/ 1 1 U,L'-1L No JONEJA et al. RDMM /5/ 1 1 0.1-16. No Cindia) DISCOVRY /11/ 1 1 0,5-20. No

PART DISC /11/ 1 1 0.5-20. No POLYNOM 7117 1 1 0,5-20. No Step tluxes only -..J

PERTURB /11/ 1 1 0,5-20. No Step fluxes onlv KAM CUSA) Solving of integral 3 3 10- 10-18. Yes

- equation /12,13/

MARTIN (USA) RDMM /5/ 1 1 10- 9-14. No M.I:.:IXN.I:.:R (West Ger. SAND-MX 111+ ! 7 6 0.2-10. Yes MORIN et al Simplif ied SAND /15/ 3 2 10- 10-11. No 1 thermal.1 epither (France) mal, 1 res. group,

34 group above 0.1 NAJZER (Yugo.) Similar to SAND /16/ 8 7 0.25-18. No NAKAMURA (Japan) Orthonorm.exp. /18/ 1 2 0.1-18. No SANGIUST (Italy) Modit. SAND-II 1171 1 1 0.1-18. No

SPECTRA /19/ 1 1 0.1-18. No SKODA (Czech.) RDMM /5/ 3 - 0.4-14. No

Eff, thresh. 1201- 3 - 0,8-7. No SERPAN (USA) SAND-II /17/ 1 1 10- 10-1s. Yes 25-group spectra TANAKA et al (Jap. Modified RDMM /21/ 13 2 0.1-18. No Graphical spectra TURI et al. ( Hun. ) Modit. SPECTRA L'2! 1 1 10- 1-18. No ZIJP (Netherland) SPECTRA /19/ 1 1

10- 10-18. SAND-II /17/ 1 1 Yes

Table 2. General characterisation of the returned spectra

i o-10 i o-9 i 0-0 i 0-1 i o-6 i o-5 1 0 -4 i o-3 1 0 -z 1 0 -I 10° 10 1 10 2

1 0 II 1 0 II ~

> w L: ........

10 14 ~ r11_____,rvk ~wt ~ +1010 u

w (j)

........ N

* * 10 9+ 1 ~ 1111 ~· II J/f \ +lo9

L: u ........ z -

10°+ A~ u .

:W / \ -t-10° z ,_,

X :::::)

10 1+/ /1 ~~~ I V \ +101

CD __J

LL

__J

CI ,_, 1-z

106+ / 1 //II ~ 1\ +10

6 w 0::: w LL LL ,_,

1 05+ / Ref erence 0 1 // 1 1 " +lo

5

1 0 4

1 1 1 ( ( 1 1 'Y V 1 1 1 1 1 11 1

1 1 0 4

10-10 10-9 10-0 10-7 10-6 10-5 10-4 10-3 10-2 10-I 10° 10 1 10 2

ENERGY IN MEV

FIG. 3. IRER-1. SPECTRR lWITH THRESHOLD RND NON-THRESHOLD DETECTORSl

~

> w z::

" u w (f)

" N

* * z:: u

" z ~

z

X ::J _J

LL

_J

er: ....... 1--z w O::'. w LL LL ....... 0

1 o-10 1 0-9 1 0-0 1 o-7 1 o-6 1 0-5 1 o-4 1 0-3 1 0-2 1 0-1 10 ° 10 1

10!?1 1 ~ 1 1 1 1 1 1 1 1 1

1011+- \ /\ l ti 1\ A i

1011 Ref erence ~ ~

109t J/f (_Al V ~

Ref erence

108t ff/ 1 r

\j

107---u /

1 1

106+1 1 1 ~

105+1 1 1 ra

10 4·-11-.._~-1-~~-+-~~-+-~~+-~~+-~~+-~~+--~~1--~~~~--+~~---

10-10 10-9 10-0 10-7 10-6 10-5 10-4 10-3 10-2 10-I 10° 10 1

1 0 2

! 10 12

+1011

+io!O

tio 9

tios

-t107

+io 6

+io 5

10 4

1 02

ENERGY IN MEV

FIG. 4. IRER-II SPECTRR CWITH THRESHOLD RND NON-THRESHOLD DETECTORSJ

\.0

> w :L ...,.,_ u w (f) ...,.,_

N

* llE :L u ...,.,_

z

z

X ::::l _j

LL

_j

a:

1-z w 0::: w LL LL

D

0 2 4 6 8 10 1 2 14 16 1 8 20 10

11 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ! 10 11

1010

109 10 9

10 8 10 6

10 7 10 7

106 1 0 6

105 10 5

1 o 4

1 1 1 1 1 1 1 1 1 1 1 1 ' 1 1 1 1 1 1 'I 1 1 1 o 4

0 2 4 6 8 10 12 14 16 18 20

ENERGY IN MEV

FIG. 5. IRER-I. SPECTRR (WITH THRESHOLO RNO NON-THRESHOLO DETECTORSJ

f--" 0

> w :L

' LJ w (j)

' N

* * :L LJ

' :z:

:z:

X =i _J

LL

_J

CI

f:z: w Q'.:

w LL LL

0

0 2 4 6 8 1 0 12 1 4 1 6 1 8 20 10

9 10

9

108 10 8

10 7 1 0

7

106

1 0 6

1 0 5 10 5

104 1 1 1 1 1 1 · 1 1 1 1 ' F 1 ~ 1="''1 1 " 1 " 1 1 1 1 10

4

0 2 4 6 8 10 12 14 16 18 20

ENERGY IN MEV

FlG. 6. lRER-11 SPECTRR (WlTH THRESHOLO RNO NON-THRESHOLO DETECTORSl

~

~

12

different versions of the SPECTRA code /19,22/ by 3, those of

the RDMM /5/ by 7 authors. Different, rnore or less known methods ( direct inversi.on, serien expansion, orthonormal expansion,

perturbation technique, effectiv-threshold concept, etc. ) have been used by 7 authors /1-4, 6-16, 18, 20, 21/. A hopeful new

method has been worked out by Kam /12,13/, in which the diffe

rence between the guess and the result spectra is characterised

by means of the following integral: o<?;)

~ rd~ ( :~~~r dE . 0

and this integral is minimised in the iteration procedure.

A large variety in the number of the used detectors could

be observed. For the I. Spectrum 24, for the II. Spectrum 22 reaction rates had been given by McElroy. All of these reactions

have been used only by one of the authors in 3 - 3 spectra for

the I. and the II& Spectrum respectively. The most of the au

thors use 5 - 15 detectors, in some cases only 3 (!) detectors have been used ( See Tables 3. and 4. ).

14 rU H 12 .µ (.)

~10 (1)

4-i 8 0

H <l)

6 .Q s 4 ;:j z

2

X

X

X

X

X

X

X

X

X X X X

X X X X

X X X X

X X X X X X

X X X X X X X X X X X X

X X X X X X X X X X X X X X X

2 4 6 8 10 12 14 16 18 20 22 24

Number of the used detectors

Table 3. The number of the used detectors for

the returned spectra for the I. Spectrum

rtJ H .µ

8 u Q) p.. (/) 6 ~ 0 4 H Q)

2 ..Cl s ;:j z

13

X X X X X X X X X

X X X X X X X X X X X X X X X X X X X X X

2 4 6 8 10 12 14 16 18 20 22

Number of the used detectors

Table 4. The number of the used detectors for

the returned spectra for the II. Spectrum

EVALUATION OF THE RETURNED SPECTRA

The differences between the returned spectra are in the

most cases very large; the ratio of the largest to the lowest

flux value et some neutron energies is over 10 in the fast end

over 1000 in the thermal end resonance region. It would be the

refore not sufficient to characterise the spectra by means of

the deviations from the reference in different energy regions;

to the characterisation of the "goodness" of the spectra more

global quantities are needed.

The following means have been used by us to the quantita

tive characterisation of the 11 goodness 11 of the spectra:

a) integrals of the deviations of spectra from the refe

rence over the neutron energy;

b) integral flux values;

c) average values of the differences between the measured

and calculated activities.

14

fg~~gE~1~_Qf_~b~-Q~Yi~iiQg_Qf_!b~-~2~~1E~_fEQ~_!b~-E~f~E~~~~

QY~E-!b~-g~~~E2g_~~~Eß;Y The normalised integrals of the squared difference between

the given spectrum and the reference, e.g. the following integ

rals:

and

E Jmax

E. min

E. min

E Jmax

E_. min

dE (2)

('.3)

are the simplest means of the quantitative characterisation of

the returned spectra. The larger the integrals, the more the

average deviation of the spectrum from the reference and consequently the worse the given spectrum is.

The integral r 1 can characterise the simple relative deviation of the spectra from the reference; the integral r 2 cha

racterises the absolute deviation from the reference spectrum;

the last integral can give a measure for the influence of the

deviation on radiation damage calculations.

In the integrals r 1 and r 2 all parts of the spectra in the

MeV region are taken into account to the same degree but the re

sonance and thermal regions are practically not included. Since that for the spectra, calculated in the full energy region one

more integral must be calculated:

=

~max

E . min

E. min

1 dE =

E

fc\Jo(u) - 4'1Cu) 12 / rmax l <Po(u) J du j du

E min

(4)

15

By means of the integrals I 1 - r 3 we can get information

about the "goodness" or the "badness" of the result spectra,

but the good or the bad qualities of the results are not determined only by the used methods, but by the number of the used

detectors, by the consistency of the used cross section set,

by the energy point structure and ( if used ) by the guess

spectrum as well. If we want to have information about the

"goodness 11 of the used method, we must separate this informatim

from others. The integrals I 1 - I 3 contain contribution of all

energy regions in question, but in the most cases only a small

number of detectors have been used ( See Tab. ). and 4. ) and

they could not cover the full energy region. Using only the

integrals I 1 - r3

a really good method could be characterised

as "bad" because of the large deviations of the spectrum from

the reference in the energy regions in which the small nurnber

of the used detectors did not give sufficient information. To

avoid this situation we have used a weighting function which

allowed us to compare the spectra with the reference only in

the region in which the used detectors contained the necessary

inforination. To do this we have used the weighting function

characterising the contribution of the flux to the activities

of the used detectors in the given energy point:

w(E)

n ~ G'. (E) ~(E)

= L l

i=1 A~

l

(5)

where A. represents the calculated activity of the i-th activai

tion detector in the ~(E) calculated spectrum,

n is the number of the activation detectors used by un

folding procedure to determine <\:i (E) „ Using this wheighting function we have calculated the in

tegrals r 4 - I 6 ( r 4 corresponds to the r 1 , I5

to the I 2 and

r 6 to the r3

, but the integrals in the numerator and in the de

nominator are weighted by w(E). ).

The two reference spectra of McElroy are given in the

energy region between 10-10 and 18 MeV, but these values could not be used as E min and E max in the inteB:rals, because fast all

16

of the returned spectra have been calculated in a smaller ener

gy range only ( See Tab. 2 )„

Since the lower and upper energy limits of the calculated

spectra are practically never above 0„5 a~d b~low 10 MeV res

pectively (See Tab„ 2„ ), for the integrals r 1 , r 2 , r 4 and r 5 E . =0.5 MeV end E =10 MeV have been choosen. min max

These integrals have been calcul2ted for all of the r~

turned spectra„ To illustrate the results for the I„ and II„

Spectrum 10 - 10 results have been selected, for which the r 5 integral has been smaller as for the other spectra, so these spectra can be called the "best" ones„ These 10 - 10 "best"

spectra and the values of the 11 , r 2 , r 4 and r 5 integrals for

them are summarised in the Tables 5. and 6.

Author Method )ign I5 I2 I4 I1

KAM Int.equ. A 1 3.87-3 1 4.27-3 1 5.73-3 1 5.70-3

KAM Int.equ. c 2 6.23-3 2 5.72-3 2 6.15-3 2 6.44-3

SANGIUST SAND-II. 3 9.34-3 30 7.34-2 3 9.00-3 6 1. 40-2

MARTIN RDMM 4 1. 50-2 3 1.94-2 32 6.29-2 34 1.10.-1

SANGIUST SPECTRA 5 1.54-2 42 1. 27-1 4 1.06-2 9 1.94-2

ZIJP

NAJZER

KAM

NAJZER

NAJZER

SPECTRA 6 2.00-2 4 2.13-2 7 1. 20- 2

ITER-2 2a 7 2.53-2 16 4.69-2 12 1. 7 5- 2

Int .• equ. B 8 2.57-2 5 2.75-2 10 1. 44-2

ITER-2 2b 9 2.64-2 14 4.59-2 8 1. 2 5- 2

ITER-2 1a 10 2.65-2 22 6.22-2 6 1. 19- 2

Table 5. The best 10 results ( among 59 ) for the

I„ Spectrum in the fast neutron energy region

4

15

5

8

10

( 0.5 - 10 MeV ) guessing from the r 5 integrals.

The third column contains an extra sign for the

given spectrum only if the given author calculated

more than one spectrum by the same method. For each

integral two numbers are given: the sequence number

1.14-2

2.29-2

1.16-2

1.63-2

2.10-2

of goodness for a given integral type and the integral

value for the given spectrum„ (3087-3 = 3.87•10-3 )

17

Author Method Sign I5 I2 I4

MARTIN RDMM 1 1. 78-2 1 1. 7 9-2 1 1. 23-2 1

JONEJA RDMM 2 2.45-2 2 1. 8 2-2 4 2.80-2 5

MEIXNER SAND-MX 2 3 2.53-2 3 1.91-2 9 3.73-2 7

ZIJP SAND-II 4 2.74-2 4 2.51-2 12 3.96-2 12

KAM Int.equ. E 5 2.97-2 5 2.83-2 25 2.52-1 25

ZIJP SPECTRA 6 3.05-2 9 3.37-2 10 3.75-2 17

BRICKA Lin.comb. 7 3,18-2 83 7.13-1 30 1. 40.J.O 30 rmod.sp.

NAJZER ITER-2 1a 8 3.22-2 7 3.33-2 15 7 • 0 5- 2 14

NAKAMURA Orth.exp. 1 9 3.25-2 8 3.34-2 11 3.93-2 8

NAJZER ITER-2 3a 0 3.31-2 10 3.38-2 3 2.73-2


II* Spectrum in the fast neutron energy region

4

( 0„5 - 10 MeV ) guessing from the r 5 integrals.

Explanation see on the Tab. 5 ( p. 16. )

I1

1. 51-2

2.67-2

3.66-2

6.78-2

2.74-1

1. 0 2-1

8.22-1

8.58-2

4.18-2

2.57-2

The integrals I3

and r 6 have been calculated only for the

full-region spectra. For these integrals Emin = 4•10-7 MeV and

E = 10 MeV have been choosen on the same reasons as in the max . case of the other integrals„ To illustrate the results for the

I. and II. Spectrum 5 - 5 results have been selected guessing

from the values of the 1 6 integral. These best spectra with

the integral values are swnmarised in the Tables 7. and 8 •

.

Author Method 1 . Sign I6 I3

KAM Int.equ. A 1 3.54-2 2 2.94-1

MARTIN RDMM 2 6.27-2 3 3.08-1

KAM Int.equ. c 3 8,13-2 5 5.84-1

KAM Int.equ. B 4 8.70-2 1 2.87-1

ZIJP SPECTRA 5 1.38-1 4 4.17-1

Tab1e 7 „ The best 5 resul ts ( among 7 ) for the L,

Spectrum in the full energy region ( 4•10-7 -

- 10 MeV ) guessing from the r 6 integrals.

Explanation see on the Tab. 5 ( p. 16. )

18

Author Method Sign I6 I3

KAM Int.equ. F 1 9.23-2 1 5.51-1

MARTIN IRDMM 2 3.20+1 2 3.70+1

['URI et al ~PECTRA 3 3.36+1 3 4.04+1

KAM Int.equ. E 4 7.66+1 4 1.06+2

ZIJP SPECTRA 5 2.15+2 5 2.26+2


II. Spectrum in the full energy region ( 4•10-7 -

- 10 MeV ) guessing from the I 6 integrals.

Explanation see on the Tab. 5. ( p. 16. )

Iu!&gr:~;J;_g~~~~ The integral fluxes for a serie of different E . values min

have been calculated for the returned spectra:

18 MeV l <j:> (E)dE

E. min

( 6)

The sequence of the individual values for the results is simi

lar to those of the integrals r 1 or I 2 ; therefore only the ave

rage values and the standard deviations calculated for all of

the spectra are shown here:

E min

MeV)

0.5

1.0

1. 5

2.0

3.0

4. 5

6.0

8.0

I • Spectrum II. Spectrum

McElroy Average int. flux McElroy Average int.

2.52+10 2.49 + 11% 2.71+8 2.65 + 16% - -1. 73+10 1. 8 2 + 7% 1.46+8 1. 50 + 7% - -1. 29+10 1. 3 2 + 8% 8.71+7 8.93 + 7% - -9,76+09 9. 39 + 7% 5.67+7 5,83 + 7% - -5.27+09 4,86 + 9% 2.55+7 2.54 + 11% - -1. 7 9+09 1. 7 8 + 22% 7.54+6 8.21 + 20% - -5.97+08 5.81 + 17% 2.09+6 2.17 + 21% - -1. 40+08 1. 41 + 28% 5.91+5 5.16 + 30% - -

Table 9. The average integral fluxes and their stan

dard deviations (1~) calculated from all spectra

flux

19

It is interesting to remark that the best results in the

energy range 1 - 3 MeV are achieved.

Detector activities ----~--------------The activities of the detectors in the returned spectra

have been calculated by us using the cross section libraI"J of

the SAND-II code. In the Tables 10. and 11. the average activity errors in respect to the measured activities, averaged over

all of detectors, over all of the used detectors, over all of

threshold detectors and over all of the used threshold detec

tors have been calculated and are shown for 10 - 10 selected spectra. These spectra have been selected guessing from the

value of the activity error, averaged over all of the used de

tectors. The spectra, by the calculation of which the number

of the used detectors has been smaller as the half of all of the detectors ( or as the half of all of the threshold detec

tors, if in the given spectrum only threshold detectors have been used ), were not taken into account in these Tables.

1 ~or all of1 For all of For all o~ For all o Author Method

J Sign 1 ~he used the 24 2 the used the 15

~etectors detectors threshold 1 detectors 1

ZIJP SPECTRA 21 3,85% 4.06% 14 3,62% KAM Int.equ. B 24 4.02% 4.02% 15 4.02% McELROY SAND-II 24 4.11% 4.11% 15 3.89% SANGIUST SPECTRA 9 4.14% - 9 4.14% SANGIUST SAND-II 9 4.14% - 9 4.14% MARTIN RDMM 15 4,33% 22.51% 7 5,39% KAM Int.equ c 24 5.24% 5.24% 15 5,34% NAKAMURA Orth.exp 12 5,28% - 12 5,28% KAM Int,equ. 24 5,43% 5. '+3 % 15 5.89% NAJZER ITER-2 ra 10 6,46% - 10 6.46%

1 - the number of the used detectors;

2 - the number of the used threshold detectors

Table 10. The average activity errors for the best

10 spectra ( among 59 ), guessing from the average

error averaged over all of the used detectors for

the I„ Spectrum„

1 1 1 1 1 1

threshold detectors

4.09% 4.02% 3.89% 9.01% 8.54%

33.14% 5,34% 6,66% 5.89% 6,60%

20

Author Method Sign 1 For all of For all of 2 For all of For all of the used the 22 the used the 13 detectors detectors threshold threshold

detectors detectors

KAM Int.equ. F 22 6,91% 6.91% 13 8.99% 8.99% NAJZER ITER-2 1b 10 7.31% - 10 7.31% 14.23% NAJZER ITER-2 1a 10 7.77% - 10 7.77% 14.59% KAM Int,equ. E 22 7.77% 7.77% 13 10.29% 10.29% KAM Int.equ. D 22 7,86% 7.86% 13 10.41% 10.41% ZIJP SPECTRA 18 8.46% 12.83% 11 6,21% 10.84% McELROY SAND-II 22 9.32% 9.32% 13 11. 22% 11. 22% ZIJP SAND-II 18 9,81% 12.92% 11 7.58% 11.47% NAJZER ITER-2 2b 10 10.25% - 10 10.25% 13.50% MARTIN

1

2

RDMM 15 10.96% 15.05% 7 3.64%

- the number of the used detectors;

- the number of the used threshold detectors

Table 11. The average activity errors for the best

10 spectra ( among 34 ), guessing from the average

error averaged over all of the used detectors for

the II. Spectrum.

13.62%

From the Tables 10. and 11 it can be seen that the average

activity errors for the II. Spectrum are essentially larger as

those for the I. Spectrum. This fact can be explained by the

presence of two „bad" detectors, e.ge detectors, for which the

cross sections and the measured activation values contradict

each other or the other detector activities. To investigate this question we have calculated the activities the detectors

averaged over all of the returned spectra. These values, to

gether with the measured ones are shown inthe Table 12„ (p.21.)

Judging from this Table, the detectors can be divided

into 4 groups: a) Threshold detectors, for which the average calculated ac

tivi ties are near to the measured value, and the standard

deviation of the calculated activities for both spectra . 1 t" 1 11 p3 1·' ) s3 2 ' ) T-4 6, ) i s re a i ve y sma : i. n, p ; \ n, p ; i \ n, p ;

Fe 54cn,p); Ni 58Cn,p); rn115Cn,n'); Th232Cn,f); Np 237Cn,f);

u238Cn,f)„

21

I. Spectrum II, Spectrum Detector

Na23(n,y)Na24

Mg24(n,p)Na24

Al27(n,a:)Na24

Al27(n,p)Mg27

P31(n,p)Si31

S32(n,p)P32

Sc45(n,y)Sc46

Ti46(n,p)Sc46

Fe54(n,p)Mn54

Mn55(n,y)Mn56

Fe56(n,p)Mn56

Fe58Cn;y)Fe59

Ni58(n,p)Co58

Co59(n,y)Co60

Cu63(n,)')Cu64

Cu63(n,a:)Co60

Measured

1. 2 2 -1 7 to . o s 3.37-17±0.24

1. 6 o -17 ±.o • o 3

9 • 4 5 - 1 7 to . 6 6

7 • s o - 1 6 ±o • 7 s i. 5 4 - 1 5 ±o • 11

2.93-16±0.21

2 • s s - 16 ±o • 2 o

1. 78 - 1 5 ±o • o 3

2 • 6 3 -17 ±o • 2 3

1. 2 5 -1 6 ±o • o 9

2.40-15±0.05

2.55-16±0.1s

4.68-16±0.32

Cu63(n,2n)Cu62 2.56-18±0.26

In115(n,n)In115 4.74-15±0.24

I127(n,2n)I126 2.44-17±0.17

Au197(n,y)Au198 4.61-15±0.32

Th232(n,f)F.P. 1.93-15±0.19

U235(n,f)F.P.

Np237(n,f)F.P.

U238(n,f)F.P.

U238(n;y )U239

4.19-14±0.os

3.43-14±0,24

6. 77-15±0 .13

3.30-15±0.16

1

8

24

41

27

13

32

5

23

30

35

5

42

8

8

Average calculated

1.24±.0,08

3,55±.0.20

1.57±.0.28

s.52±.i.32

7. 9 3 ±o. 4 3

i. 4 3 ±o. 10

3. 02 ±o. 04

2,77±0.11

1. s 4 ±.o. 01

2. 5 s ±o. 13

1. 20 ±o. 03

2,39±0.16

3. o 1±o.63

4.61±0.07

1s 3,3o±i,35

45 4,73±0.27

15 2.08±0.39

8 4,32±0.05

24 i,74±0.os

18

40

26

6

4,24±0.14

3,75±0.28

7.02±0.28

3,57±0.09

Measured 1 Average

, alculated

2.61-18±.0.13 7

1.51-19"to.o5 ~5

5.8s-2o"to.1s bg

6. 58-18 ±o. 46 118

4.45-11±0.22 5

1.35-18±0.08 h8

9,09-18±.0.45 tz7

7.07-17±0.70 7

6.97-2o±i.05 122 9 • 6 2 - 18 ±o • 4 s 5

1. 3 4 - 1 7 ±.o • o 3 3 1

1. o 5-16 ±o • 1 o 7

7,93-17±0.40 7

6.02-20±.i.50 10

3.49-17:!:0.17 26

1. 22-19±0.12 14

1,09-15±0.04 7

1.07-17±0.09 18

2.20-15±0.04 8

3.89-16±0.27 27

4.93-11±0.15 24

2.59m.21

i.39m.23

5.83±o.91

7,26±o.61

4,23±o.42

1.26"!:o.o8

9,2s±o.11

7. 13 ±.o. 3 3

8,86±1.23

9. 51 ±.o. 31

1. 3 2 ±o. 08

1. 20±0 .16

8. 23±0. 60

3.oo±o.49

3,5s±o.14

1.04±0.18

i.14±0.20

1.12±0.05

2,05±0.13

3 • 9 2 ±o. 2 9

4.88±0.29

Pu239(n,f)F,P. 6.19-14±0.62 s 5.1s±o.22 1.59-15±0.24 7 1,33±0.09

1 - the number of the spectra, in the unfolding procedure for which

the given detector have been used

Table 12e The rneasured actiYities and the averaged

.calculated activities of the detectors for the

Ie and II. Spectrum

22

b) Threshold detectors, for which the average calculated activities are not so near to the measured ones, or the standard deviation of the calculated activities is larger: Mg24cn,p); Al27Cn,p); A127cn,a )„

c) Threshold detectors, for which the difference between the measured and the average calculate.d activities, or the standard deviation of the calculated activities is very

. 56( ) 63( ) 63( ) 127 I' ) large. Fe n,p ; Cu n;y ; Cu n, 2n , I \n, 2n • For the detactors Fe 56Cn,p) and Cu63(n,y) in the II. Spectrum a great. discrepancy can be obsarved between the measured and the average calculated activi ties, the acti.vi ties of these detectora contradict to those of the others„ In the case of the Fe56(n,p) raaction the measured reaction rate in the~ II. Spectrum is probably wrang, since in the I. Spectrum no discrepancy has been observed. In the case of the cu63(n,y) no data exist for the I„ Spectrum, from which conclusions could be drawn, here the cross sections and/or the measured activity can be wrong.

d) Non-thr~shold detectors: Na 23 Cn,Y); sc45Cn,Y); Mn55Cn,Y); Fe58(n,y); co5 9cn,y); cu63cn,y); Au197cn,Y); u235(n,f); u238(n,y); Pu239(n,f)„ These detectors have been used by a very limited number of authors using mainly the crosH section library of the SAND-II code. The deviation of the average calculated activities from the measured ones and the standard deviation of the calculated activities are generally low. There are two exceptions: the co59(n,Y) and the Au 197 (n, y) reactions ,. there was probably a trivial error irr the cross sections used by one of the authors, which caused the discrepancies in these two ca-ses.

23

DISCUSSION AND CONCLUSIONS

With the aid of the arrangement of the International Intercomparison of Neutron Spectra Evaluation Methods Using Acti

vation Detectors the Working Group on Reactor Radiation Measure

ments of the IAEA wanted to have a good picture of the state-of

-art in this field0 This goal has only partly been reached„ The differences between the returned spectra are very big. It can

be understood if we take into account the following circumstan

ces: 1. There exists an infinite number of different spectra

satisfying exactly the activity equations; the number of the

spectra satisfying the activity equations only within some error is infinite as well. To help to choice the best answer

from an infinite number of possible spectra generally a properly choosen guess spectrum is needed. The participants have got only

the reaction rate sets without any physical information or guess

spectrum from the organisators; as a result of this insufficien

cy of the input data the returned results are broader distributed and have a larger errorthan itcould be expected in a real

physical case.

2. The cross sections play a very great part in the un

folding procedure. Non-consistent cross section sets may result

very big oscillations. If the unfolding is accomplished by

means of essentially smaller number of detectors as given by the

organisators, then important parts of the information contained in the reaction rate set can be lost. As it can be seen on the

Tables 3. and 4., the most participants have used only 5 - 10

detectors from 24 and 22 respectively - the most laboratories

are not in the disposal of a sufficient cross section library.

The cross sections have been choosen from different sources and

are often inconsistent. The fact of the using of different cross section sets, containing often only a very small number of de

tectors has made the evaluation and the intercomparison of the

returned spectra very difficult.

')„ The participants have used very different energy point

systems: fo!" example in the SAND-II programme 620 neutron groups

are used, in the different versions of the SPECTRA code 50 - 100

24

points are used and the flux is supposed to vary linearly be

tween the points, in the RDMM code the flux is supposed to be

continuous, some authors calculate only few-group ( 11 - 20 ) spectra. The in:fluence of the energy point number on the results

has up to now not been satisfying investigated„

In light of these circumstances it can not be unexpected,

that the best results have been sent by the participants, who

could use a guess spectrum library and a consistent cross sec

tion set ( Kam, Zijp, Martin )„ All of these participants have

used the cross section library of the SAND-II code, Kam and

Zijp have used the guess spectrum library of the SAND-II code

as well. These authors have used different codes ( Kam - Sol

ving of Integral Equation, Zijp - both SAND-II and SPECTRA,

Martin - RDMM ), but practically the same cross section set, and so could get the best results„

The SAND-II and SPECTRA codes have been known up to now as a suitable means to unfold neutron spectra, the goodness of

these codes· have been demonstrated and now as well„ The RDMM

code has been used here for the first time not only in the fast, but in the resonance region as well by Martin„ The results are good, as concerns the integrals of the deviation from the refe

rence and the activity errors, but the spectra are too smooth;

the RDMlVI code can not be used when narrow deeps or high peaks

occur. A new method has been worked out by Kam, it has to be tested by means of further comparison with other programmes on

different spectra„

Not all of the questions could be investigated by means

of the returned spectra. Judging from them a state has been

reached, when not the used programmes and methods, but the cross sections and the guess spectra seem to be more important„

This intercomparison could give a partly coarse picture

of the state-of-art in the spectrum unfolding; to investigate

the questions in more details a new intercomparison is necessary

in which by all of the participants the same cross section set,

the same guess spectrum and possibly the same energy point sys

tem will be used„

25

LITERATUR& 1„ BRICKA, M„, BENEZECH, G., DOLIAS, MMe„ M„, "High-energy par

ticles spectrometry using activation detectors", Symposium on Accelerator Dosimetry, Brookhaven ( Nov„ 1965 )„

2. BRICKA, M., NGUYEN VAN DAT, PORTHEOS, L„, Le spectrometre neutrons a activation SNAC ( The activation neutron spectrometer SNAC ), CEA Report R„ 4226 (1971)„

3„ FASSO, A„, BRICKA, M., NGU'.LEN VAN DAT, "An extension of the model spectra rnethod for neutron spectrometry with multiple passive detectors" XVI. National Congress of the Italian Association for Health Physics and Radiation Protection„

4 „ BUXEROLLE, M„, Neutron spectrometry by means of a mul tidetector system (in French ), Note CEA.N-1468, July 1971.

5„ DiCOLA, G., ROTA, A„, "RDMM, a code for fast neutron spectra determination by activation analysis", EUR 2985e (1966)„

6„ GRANCEA, I., CUCULEANU, V., IFA-FR-65-1968 7„ GRANCEA, I„, CUCULEANU, V., IOSIF, V„, IFA-FR-77-1969

0 8. PURICA, I., CUCULEANU, V., Rev. Roum. Phys„ Tome 14, N- 7, pp„ 587~594, 1969„

9„ CUCULEANU, Ve, Rev. Roum. Phys„ Tarne 12, N2 6, pp. 603-614,

1969. 10„ KORTHAUS, E„, KFK-1141 (1970) 11. JONEJA, O„P„, RAlVrAKRISHUA, D„v.s„, NAVALKAR, M„P. "Contri

bution to this Intercomparison" ( unpublished )„

12„ STALLMANN, F„W„, "Numerical Solution of Integral Equations„,

Numer„ Math„ 15, 297-305 ( 1970) 13 „ KAM, F „B„Ko, "Contri but ion to this Intercornparison° ( unpub

lished )„

14„ MEIXNER, CH„, Jül-726-RX„ 45,. McELROY, W„N., BERG, S„, GIGAS, G„, Nucl. Sei„ Eng. 27, 533-

541, 1967„ th 16„ NAJZER, M„ et al„, "Proceedings of the XIV Conference on

Electronics, Telecommunications, Automatisation and Nuclear Engineering, Sarajevo, June 1970 11 „

17„ McELROY, W„N., BERG, s„, "A Computer Automated Iterative

Method for Neutron Flux Spectra Determination", Vol„ I-IV„,

AFWL-TR-67-41 (1967)„ 18. NAKAMURA, T„, Contribution to this Intercomparison ( unpub-

26

lished )„

19„ GREER, C„R., HALBLEIB, J„A., WALKER, J.V„, SC-RR-67-746,

1967„ 20„ SITVA, ~.1ANES, AE 2551 /Dok eo des ( Skoda-report in Czech ) " 21„ MATSUI, T., YAW~DA, T., JAERI-Memo 3000, 1968„ ( in Japa

nese ) 22. FISCHER, A „ , TURI, L „ , "The RFSP programrne f or unfolding

neutron spectra from activation data" INDC(HUN)-8/U„ May, 1972„

23 „ HASENCLEVER, B„, "I „A „R„A „ Intercomparison of Neutron Spectra Evaluation Methods Using Activation Detectors. Preliminary Compilation of the Returns„, 3rd Meeting o:f the IAEA Working Group on Reactor Radiation Measurements, Seattle, 2-3„ Nov„ 1972.

27

A P P E N D I X

This Appendix contains all the returned spectra.

':'he used method is printed as given by the authors„ The

well-known methods ( RDMTuI, SPECTRA, SAND-II ) are not printed,

but mentioned.

The spectra are gi ven in graphical form. The fiw~re s con

tain the flux, the reference flux, and the 5% and 95% activity

ranges for the detectors used by the unfolding of the given

spectrum„

On the figures the following quantities are given:

1) The few-group flux ratio.

The few-group fluxes were calculated by us by simple

integration of the originally given fluxes over the

energy between the group-boundaries„ The few-group

referPnce flux was ~alculated by the same method.

Using the few-group flux ratio we could; avo~.d the

too large effects of the oscillations.

2) Integral fluxes.

3) The integrals I 1 - I 6 m2ntioned on the pp. 14 - 16

for the originally given fluxAs and for the few-group

fluxes.

4) The average activity errors rl8ntioned on the p. 19:

A1 - average over all of the 24 / f or the I. :=_~l)8 C -~ rUEl \..

22 / f or the II. Spectrum ) d2tectors; or \..

A2 - average over all of the 15 / f or th9 I. Spectrum \..

)

)

13 / f or the II. Spectrum ) threshoJd r'letgctors ; or \..

A3 - average over all of the used cetectors;

A4 average over all of the used threshold dJtectors.

For tl:1e full energy region spectra an extra figure is given in

logari thmic scale. ?or the fast-region spectra the integrals I3'

I 6 and the average aKtivity error for all of the d2tBctors, A1 ,

were not calculatea.

Me BRICKA, Me MORGUES

CEN CADARACHE, FRANCE

METHOD:

NETHODE DE SPECTR0~1ETRIE

28

La. methode des spectres modeles a ete dcveloppee pour l'exploitation

des donnees du spectrornetre neutron a activation SNAC .("1J .["2J L3J. On ad.met que le spectre inconnu, ~ (E) peut ~tre represente par une combinai

son lineaire de spectres elementaires, ou spectres modales :

n

p (E) = 2 n:LFi (E)

1

( 1)

L'introduction, comme modales, de formes de spectres connues : maxwellien,

spectre en K/E, spectre de fission, permet d'apporter au systeme de donnees des

informations supplementaires. En utilisant uno serie de segments de droites

horizontaux on obtient l'histogramme.

La reponse d'un detecteur J est donnee par la relation

n I CTj (E) • Pi (E) dE Aj =2 a:.Kj (2)

1

Kj etant le coefficient d'etalonnago du detecteur - egal a 1 si Aj represente

le taux de reaction du detecteur J. L1 integrale correspond au taux de reaction

du detecteur J pour le modele Pi. Soit Rij la valeur de cette integrale qui

peut ~tre calculee, le detecteur et lo modele ctant definis.

La reponse du detecteur j prend la forme :

Aj n

= 2 <Xi.Rij. 1

(3)

L'cnsemble des reponses des m detecteurs peut, en definitive ~tre represent~

par l'equation matricielle.

Cette equation possedo une Solution unique si n = m.

Ello peut ~tre trai tce par la methode des moindres carres si n <::'.: m.

29

Si de nombreux detecteurs sont utilises, la gamme des scnsibilites peut ~tre

assez grande. La methode des moindres carres, dans ce cas, ne tient pa.s co~pte

des taux de sensibilite les plus faibles. Il est alors necessaire de ponderer

les reponses.

L'equation matricielle (4) sera remplacee par l'equation :

1 = cti • Ri.i Aj

(5)

11 est ml*no possible de tenir compte de la precision, Ej% des mesures, en

traitant 1 1 equation :

1 Rij (6)

Aj • ~),

PROGilA}ii-IE DE CALCUL

L1 6quation matricielle (4) peut ~tre traitce par le programme SESR 590.

La matrice \Rij\ peut ~tre :

soi t calculee par l' ordina teur a partir des donnees () j (E) et Pi (E),

soit introduite directement.

La prograrome prevoit,outre la determination des c:d. :

- le calcul de la fluence totale ou de la fluence pour des band.es d•energie

donnees,

- le calcul de toutes integrales de la forme.

I i= JE;i {> (E). D(E) dE

E1

- la. normalisation du spectre a 1 neutron.cm-2 et son trace sur BENSO~.

La temps machine, sur IBH 360/65 est de l'ordre de 20 secondes.

30

Translation:

"Dr·~-'-"'''D'''''·,-. .... , (ci,1,'1") d'•ta rl 3J o..>,l :...•..,...,L...1...;11t:.:·ll...;..i. ,.).• .. ·'--' '-1.·· L - (i)

can 1:-::: rcpresc.ntccl oy a. linear combinaticn of eleoentary s:;:>ectra or rnodcl sp·:;st:-·~·:

n

f (E) = :> 1

o:i.Fi (E) (1)

1

B:ir int:c·od"...lcing knoon forms of spectrap such ac tho MaxweJ.lian, tho K/E and

the fiss:i.or, spcctra, a.c modeln? it is i;ossible to add supplerr:entar,f

infor;.:::aticn to thc data s,ysterr.. The histoe;ram is obtained by usinc a serie:;-

of seg-r;;cntr:> of f1orizuntn.l stra.ight lincs.

The respo:nse of detector J is givcn by tte reln.tion

Aj = ~~ o:.Kj I <Yj {E) .Fi {E) dE (2)

Herc Kj is thc oaliln:"'<l.tion cocfficiont of the detector a,'1d eqnal to unity if

Aj repre:3ents th0 rca.ction rate of detector J.

to thc r.:;;action rate of detoctor J for model P.i.

The intcc;ral co1·responds

Let Hij bo thc value of

this interrral~ which oan bc oalculatcd s:i.nce thc detector und the model are

tlefined.

The respom:e of dctector j takes the form:

n

Aj -2 cd.Rij. - :__.J 1

(3)

( 4)

If C:... lar~~o rr.:l",'.~1(::-Y'I v ..... f /.Jri.t.·-.· 0,,~1~r.-! :-'!.-:-·•"'.· ,,~~'.·.r.:. ~ ..... ), (""r·..-,r--+~"1''1)0 .J.„„ ...... r-,..,.,..., •. - c·~ 1·· ~ - .... _ ..... _..... - u_ ... - r ....... ~ ..... L4~ . , 1.-„~:..., .,_) · .. t.._„ vJ.". '-j ,J,.t„„1:.';l- ~._ ,. Ja

31

Matrix equation (4) 1,;ill bo rcplaccd ·by the

=

It i::; cvcn po~;~_;).1le to t:1.ke account of ·f.hü precision

1 o:i

J.!2.trix cqua.t~i.w ( 4) can bc processcd by the SESR 590 pro5::::<:..rn::;.

Matrix IRij\ cet.n b0:

Either calculated by cor.1puter from data crj(E) and Fi(E);

Or introduced directly„

The prograx;i.rne involves, apart from thc detcrmination of d:

The calculation of total flucr:cc or of the fluence for the

givcn enorgy band.s;

The calculation of all integrals o.f the form:

~ I t= j . f {B) • D(E) dE

E1

(5)

(6)

-2 Hormalization of the spectrum to 1 neutron x cm and i ts gra.ph

on Benson papcr„

The computa:tion time, in the case cf rmr 360/65, is of the ordor of

20 sec„

SPECTRA PROCESSED: I„ Spectrum ( 3 results ) II. Spectrum ( 2 results )

I.1. - without weighting ( Fig. 7 and 8. ) I.2. - with weighting corresponding to the mea~urement accu

racy ( Fig. 9 and 10.) I.3. - with weighting corresponding to the measurement accu

racy and with smoothing ( Fig. 11 and 12. )

32

II„1„ - without weighting ( Fig„ 13 and 14„ ) II.2„ - with weighting correponding to the measurement accu

racy ( Fig„ 15 and 16„ ).

REPRESENTATION MODE OF THE RESULTS: 89-group spectra as step fluxes for ~(u) = liJ:~(E)„

ENERGY REGION: 10-8 - 20. MeV

GUESS SPECTRUM LIBRARY: No.

REMARKS: No„

33

0 2 4 6 8 10 1 2 1 4 1 6 18 1011 1011

> w L:

"' LJ 1010 w (f)

"' N

* MG24lNPlNA24

* 1 09 AL27lNHElNA24 10

9

L: LJ

FE561NPlMN56

"' !1271N2NlI126

z 1461NPJSC46

z 108

108

X :::J U2381NF lF. P. _J 1NI151 N l IN115M LL

107 NP2371NFJ • p. 10

7

_J AU1971NGJAU198 IT CU63!NGJCU64

PU2391NFJF.P 1-z FE581NGJFE59

1 06 10

6 w U2351NFJf ,p, ()'.'. NA231NGJNA24 w LL SC451NGJSC46 LL C0591NGJC060

0 ·1 05 1 0

5

0 2 4 6 8 10 1 2 1 4 16 18

ENERGY 1 N MEV

ENERGY GROUP FLUX/REF. FLUX ENERGY INTEGRAL FLUX

0. 5 - 1 .o o.302 o.5 2·164E+10 1 . 0 - 1 ,5 1 . 426 1 .o 1 .928E+10 1 ,5 - 2.0 1 .175 1 . 5 1 . 300E + 10 2 .o - 3.0 0.851 2.0 9.263E+09 3. 0 - 4,5 0.893 3,0 5.439E+09 4. 5 - 6.0 1 . 545 4,5 2.331E+09 6 .o - 8.o 2.049 6.0 4 .840E+08 8.0-10.0 8.o

10.0-14.0 10.0 14.0-18.0 96.071 14. 0 1.314E+08

CHARACTERISTIC INTEGRALS AVERAGED ACTIVITY DEVIATIONS

I 1 I z I 3 I4 I 5 16 A1 Az A3 A4

ORIGINAL 4.152 o.502 5.41E+8 -6.877 o.234 5.86E+9 234.7)1 337. 13 81. 07% 89.01%

FEW-GR. 2.758 Q.325 1 . 91 E +8 2. 405 Q.252 1 .29E+9

MR. BRICKR, FRRNCE. W!THOUT WEIGHTING

FIG, 7

1 o-10 1 o-s 1 o-8 1 o-7 10-6 10-s 1 o-4 10-3 1 0-2 10-1 10° 10 1 1 0 2

10111 1

1 1 1 1 I 1 1 1 1 1 1

1

1011 ~

1\ > w ::;::: "-(_)

101-4-- 1 1 1\ ~ 1 ~\ +iolO w

(f)

"-N ll(

llE ::;::: (_)

109+ 1 1 1/ \1

, \"! +io

9 "-z

lo

z ~ / F ES6' "Pl "~' +o· <.L -.::!- 1127(N2Nlll2 1 t<\ X 10 8 :::J Tl46(NPJSC46 c _J S32lNPJP32 c::::J e·, LL FES4lNPJMNS4 ~

µ.

_J NIS8lNPJCOS8 er: TH232(NfJf.P. ~

10 7 U238( NF JF .P. c:=J 1 II +io1

1-z IN!JS(NNJINl!SM c=::::J w NP237lNFJf.P. c::===J 0::: RU 97(NGJRU198 w CU63( CU64 LL LL ~

106+ FES8l GJFqsg 1 1 +ios 0 U23S F JF.

NA23lN NA24 SC4SlN JSC46 COS9l GJC060

1 0 5 1 0 s 1 o-10 10-9 1 o-8 1 o-7 1 o-s 1 o-s 1 o- 4 1 o-3 1 0-2 1 0-1 10° 10

1 1 0

2

ENERGY IN MEV

MR. BRICKR. FRRNCE. WITHOUT WEIGHTING

35

0 2 4 6 8 1 0 12 1 4 16 1 8 1 o11 1 Ü II

> w :L:

---,

"' 1010 1010 LJ w (f)

"' N )1( 1127( N2N l 1126 )1(

109 MG24(NPlNA24 10

9

:L: AL27(NHEINA24 LJ

"' FE56!NPIMN56

z Tl46(NPISC46 PIP32

z 1 ÜB FE 4 ( IMN54 1 08

NI5 (NP l 58 TH2 2( NF IF.

X ::::J U23 _j IN115<NNlIN115M LL

107 NP237(Nf Jf ,p, 10

7

_j

a:

f-z

106 1 06

LLJ 0:::: LLJ LL LL

D 105

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o 0.337 o.5 3.029E+10 1 . 0 - 1 ,5 3,543 1 .o 2.765E+10 1 . 5 - 2.0 2 .124 1 . 5 1 .163E+10 2. 0 - 3.0 2.0 4.867E+09 3. 0 - 4. 5 o.468 3.0 4.928E+09 4. 5 - 6.0 1 ,577 4,5 3.299E+09 6. 0 - 8.o 2.590 6.0 1 .294E+09 8.0-10.0 0. 486 8.o 1 . 111 E+08

10.0-14.0 1 . 705 10.0 6.396E+07 14.0-18°0 14. 0

CHARACTERISTIC INTEGRALS RVERAGED RCTIVITY DEVIRTIONS

11 1 2 l 3 14 l 5 l 5 R1 A2 R3 R4

ORIGINAL 2.010 3. 181 2.69E+8 5,553 10. [ 15 2.77E+9 36.94% 31 . 61 % 37.44% 29.50%

FEW-GR. 1 . 271 1 .770 9.56E+7 2.757 4,093 6.44E+8

MH. ~RllKR. FRRNCE. WITH WEIGHTING

FIG, 9

10-10 10-9 1 0-0 10-7 1 o-6 1 0-5 10-4 1 0-3

1 0 l ' l 1 1 1 1 1 1 1 1 1 1 1 1

> w :L "--u w (/)

101 Q_f-

"--N

* * :L u "--

-~ 109

z ~

z \0 ........ t<\

X ::J

-f-10 8

_J

LL

_J

er: ........ f- -~ 107 z w 0::: w LL AU 197C IC JAU198 LL PU239CN JF p. ........ 0

-~ CU63CN JCU6~ U235CN JF.f.

10 6

NA23CNG NA24 5C45CN JSC46

059C GJC060

1 1 1 1 1 1 1 1 1 1 1 1 10 5

10-10 1 o-9 1 o-8 1 0-1 1 o-6 1 0-5 1 o-4 1 0-3

MR. BRICKR. FRRNCE. WITH WEIGHTING

1 0-2 1 0- 1 10° 101 1 1 1 1 1 1 1 1

1\

(" \ I\ \

112 °C N2~ ) 112 0 MG24C NPJN 2 tJ AL27C ~HE ll A'4 10 FE56C 1 p JM~ 56 cp

T 146C Nf lSC46 IC S32CNP P32

§~ FE54CNF lMN5 Nl58CNPJC 58 -

TH232CNFJF P. c= p U238 C NF J F .1 • c= =:J

1N11 5 C NN J 1 N n15M iC - =i NP237CNFJF.P. FE58CNGJFE5 >----

1 1 1 1 1 1 1 1

1 0-2 1 0- 1 1 0° 101

102

10 11

- - 1010

- f- 109

- - 1 08

- - 107

-~ 1 06

10 5

1 02

ENERGY IN MEV

0

0 ~~

""''

> w L::

' LJ w (f)

' N

* * L:: LJ

' z

z

X ::::> _J

LL

_J

a::

fz w Q:::'. w LL LL

D

37

0 2 4 6 8 10 12 14 16

.___ ___ _, CU63( N2N lCU62 .__ _____ __, I 127 ( N2N l 1126

~---------~ MG24(NPlNA24

'-----------____J AL27 ( NHE l NA2 4 '--------------~ FE56(NPlMN56

--~~~~~~~~~~~? AL27( NP lMG27 .- TI46(NPlSC46 '--------""'<1--' S32lNPlP32 c========~s FE54lNPlMN54

P lS 131 NPlC058

.___ ________ ____, TH232 (

'---------___, U238( NF lF ,p. ~--------' INll5lNNlIN115M

'-----------~ NP237( NF lF ,p. 10 7'-f:=======:::i U238(NGlU239

n----------' PU239( NF lF ,p. 1-------' FE58(NGlFE59 1-------~ CU63(NGlCU64 1----------' U235( NF lF ,p.

1 0 6'-t:::::===:::i AU 197 (NO l AU 198 C059(NGlC060

1--------' NA23( NO lNA24 1-----' SC45( NO lSC46

18

1010

5 10 5·---t-~-1-~+---11---+~-t-~-t-~+---1~-+~-+-~+-~1---+~-t-~-1-~+---"ll---"+-+-A-"~~

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o o.594 0.5 2.187E+l0

1 . 0 - 1 ,5 o.929 1 .o 1 .722E+10

l • 5 - 2.0 1 . 025 1 ,5 1.314E+10

2. 0 - 3,0 0.996 2.0 9.874E+09

3. 0 - 4,5 o.975 3.0 5.399E+09

4. 5 - 6.0 1 .125 4 ,5 2.003E+09

6. 0 - 8.0 l .061 6.0 6.579E+OB

8.0-10.0 l . 090 ß,Q 1.732E+OB

10.0-14.0 1 . 4 94 10 .o 6.749E+07

14.0-18.0 4.009 14. 0 5.482E+06

CHARACTERlSTIC INTEGRALS AVERAGEO ACTIVITY OEVIATIONS

I 1 I 2 1 3 1 4 I s l s A1 A2 A3 A4

ORIGINAL 0.037 0. 1I4 7.88E+8 0.033 0. 123 2.73E+10 37.69% 25.89% 37.69% 25.89%

FEW-GR. o.014 o.097 2.24E+7 o.OI9 0. 104 1.28E+8

MR. BR!CKR. FRRNCE. WJTH WEIGHTING RNn WITH RMnOTHING

FlG. 11

i o-10 1 o-9 10-8 10-7 1 o-6 10-5 10-4 10-3 10-2 1 0-1 10° 10

1 102 1 Ü II 1 Ü II

~

> w :L: '-.. u

1014 1 1 1 \ / -~ +io!O w

(J)

'-.. N llE llE

:L: u

109t

1 1 1 V 1 MG24lNPJNR24 \o +ios '-..

z RL27lNHEJNR24 FE56lNPJMN56

z 1 1 1 1 / 1 1 RL27lNPJMG27 Tl46lNPJSC46

~ t!O' N

X 108 'V S32lNPJP32

CO ::::J FE54lNPJMN54 !<"'\ __J P3!lNPJSl3! '-' LL N!58lNPJC058 H

rx. __J TH232lNFJf.P. c::::::J a: U238lNFJf .P. c:=i ~

107 INl!SlNNJINllSM c==::J ~ +io 1 f-z P237lNFJf.P. w U238lN JU239 et:'. w -i FE58lNGJF 5 LL LL CU63lNGJ U6 ~ 1 Ü 6 U235 l NF F · P ~ \1 106 0

RU197l N JRU19 C059( l C060 NR23 GJNR24 SC4 NGJSC46

105 105 i o-10 1 o-9 1 o-8 1 0-1 1 o-6 1 o-5 1 o-4 10-3 10-2 1 0-1

10° 101

102

ENERGY IN MEV

MR. BRICKR. FRRNCE. WITH WEIGHTING RNO WITH SMOOTHING

39

0 2 4 6 8 10 12 14 16 18 10 9-Jrr-+----l!---+~-t-~+--+~--+-~+-....... ~--l-~-J.--~+.-.......+~-l--~-l-----J~-l-~=+-10 9

> w :L

" LJ w (f)

" N

* * :L LJ

" z

z

X :::J _J

LL

_J

0:

f-z w er:: w LL LL

~----------' 1N115 '--------1 NP237( NF IF ,p.

,__ ___ __, PU239( NF IF ,p. AU197(NGJAU19B

CU63(NGJCU64 10 5 FE5B(NGIFE59

,___~ U235( NF lF ,p. C059(NGIC060 SC45(NGJSC46

D 10 4-+~+-~r--+~-1-~+---t~-+~-1-~t---+~-1-~+--+__;~~+-~f..--.--+~~

0 2 4 6 8 1 0 12 1 4 16 18

ENERGY 1 N MEV


0. 5 - 1 .o 1 .220 0.5 2.B34E+OB 1 . 0 - 1 . 5 Q.63B 1 .o 1 . 299E +OB 1 . 5 - 2.0 Q.B97 1 . 5 9.252E+07 2. 0 - 3.0 1 . 26B 2.0 6.532E+07 3. 0 - 4,5 Q.9Bl 3.0 2.576E+07 4. 5 - 6.0 0.271 4,5 B.OB5E+06 6. 0 - B.o 1. 39B 6.0 6.607E+06 B.O- 10.0 5,722 B.O 4.507E+06

10.0- 14.0 19. 145 10. 0 2°221E+06 14.0- lB.O 14. 0

CHARRCTER IST I C INTEGRALS AVERAGED ACTIV!TY OEVIATIONS

I 1 I 2 I 3 I 4 I 5 I 6

ORIGINAL 7.23I 0 .1 OB 4B.46I 5,799 0. 103 5.0BE+2 114. 58 177. 1 s 111 ,93

FEW-GR. 4.829 Q.061 2.607 4.067 Q.055 9°096

MR. BR 1 CKR, FRRNr.E. W I THnllT WF 1r.HT1 ~IG

FIG. 13

104

1 o-10 1 o-9 10-8 1 0-1 10-6 10-5 1 o-4 1 o-3 1 0-2 1 0-1 10° 101 102 1012 1012

~

> w ::c '-

10 13+ 1 1 1 /\ \ +io11 (__)

w (f)

'-N

* * 1014- 1 rl \1 ~ -~ +10

10 ::c /\._

(__)

'-z ~

~ "'2"'1126 1 0 z 10

9 L NHElNR24 [] t109

-tj- ~ G24 ( l NR24 [] ES6lNP NS6 CJ "<t

X 6lNPlSC c::=:=J ::J

_J S32lNPlP32 '.:::::::]

+io0 0

LL 108 FES4lNPlMNS4 c:=:=:J „_, NJS8lNPlCOS8 ~ i: ....

_J

a: TH232lNFJF.P. ~ U238(NFJF.P. 1- !Nl 15( NN l IN! !SM z w 10

7 NP237(NFJF.P. ~ +io1

0:::: w PU239lNFJf.p.

LL LL ~ _µsacNGlFES9 0 10 6

23lNGlNR24 1 ~"' +io6

23S(NFlF-P. OS9lNGlC060 C4SlNGlSC46

1 05

1 1 1 1 1

1 1 1 1 1 1 1 ) 1

1 l 0 5

1 o-10 10-9 1 0-0 1 0-1 10-6 1 o-5 10-4 1 0-3 1 0-2 1 0-1 1 0° 101 102

ENERGY IN MEV

MR. BRICKR. FRRNCE. WITHOUT WEIGHTING

41

0 2 4 6 8 1 0 1 2 14 1 6 1 8 10 9 10 9

> w L:

" u w 1 OB 1 OB (f)

" N )II I 127( N2NJ I 126

* MG24(NPJNA24 :>::: AL27(NHEJNA24 u

" 10 7 FE56(NPJMN56 107 z TI46(NPJSC46

z

X 10 6

::J 106 _J

LL

_J

er: 97(NGJAUl98

f-3(NGJCU64

z 105 FE58(NGJFE59 1 0 5

w 3(NGJNA24 O'.'. U235(NFJF.P. w 9(NGJC060 LL LL

D 1 0 4 1 0 4

0 2 4 6 8 1 0 12 1 4 16 18

ENERGY IN MEV


0. 5 - 1 .o 0 °132 o.5 1 .696E+08 1 . 0 - 1 ,5 o.993 1 .o 1 .529E+08 1 . 5 - 2.0 1 . J 25 1 . 5 9.466E+07 2. 0 - 3,0 1 . 048 2.0 6.052E+07 3. 0 - 4,5 1 .0! 4 3.0 2.782E+07 4. 5 - 5.0 1 .041 4,5 9.540E+06 6 .o - 8.o 2.242 6.0 3.874E+06 5.0-10.0 0. 511 5.0 5.050E+05

10.0-14.0 1 . 704 10.0 3.007E+05 14.0-18.0 14 .o

CHARACTERISTIC INTEGRALS RVERRGED ACT!VITY DEVIRTIONS

I 1 I 2 I 3 I 4 I s I s R1 Rz R3 R4

ORIGINAL 0.522 o.713 52 .111 1 . 398 o.032 5.31E+2 25. 97% 27.07% 24.70% 26.98%

FEW-GR. 0.416 o.573 2.513 0. 462 0.235 9.618

MR. BR!CKR. FRANC[. WITH WEIGHllNG

FIG. 15

1 o-10 1 0- 9 1 0-0 1 o-7 1 0 -B 1 0-5 1 o-4 1 0-3 1 0-2 1 0- 1 10° 101

1 0 2

1012 1012 -> w :L '-.

1011+- 1 1 1 /\ '\ +io11 LJ

w cn '-. N

* * 10 14 1 }--J 1 \ 1 ~"~ +io!O :L /\-._

LJ '-. z -

109+ V 1 1 \V 1 ~ ~~!N2Nll126 D N G2 PlNR24 D

tl09 -.;;!- z

. D

r'Ns<NPtsC~ ~ '° X

10•+ / V

'\ =i _J S32!NPlP 2 c=::J

+ioa <:.-' LL FES~!NPlM 54 c:::::J H

t.ITCOtt.IDll'"' eo ,---, >=.< _J ([ ....... 1--z

107t 1 1 1 NP237!NFlF-~- ~ +107 w

0::: PU2 9!NFJF. w RU!97fNGlRU19s° LL LL ....... 0 10 6

t23rNGlNR24 1 1 tios

235!NFlf.p. 059!NGlC060 C45(NGJSC46

105

1 1 \ 1 1

1 1 1 1 1 1 1

11 ~ 1 105

1 o-10 1 0-9 10-8 1 o-7 1 o-s 1 0-5 1 o- 4 1 o-3 1 0-2 1 0-1 10° 101

102

ENERGY IN MEV

MR. BRICKR. FRRNCE. WIJH WEIGHTING

43

M„ BUXEROLLE

CEN CADARACHE, FRANCE

METHOD:

Le programme de calcul utilise la methode d 9inversion de

matrice.

On dispose d'une suite ordonnee de m detecteurs idantifies

par l'indice j et dont la reponse spsctrale (}".. (E) ast connua;

soit ~ (E} le spectre recharche qui doit ~tre n~l a l'exterieur das

bornes inferieure Ern et superieure EM des energies E, 1 9observablc

Aj du detecteur de rang j (activite induite) est donne par :

( 1 ) Aj = JEM

o1 (E) e cP(E) „ dE

Ern

On represente4(E) par une ordonnea constante hi sur un

intervnlle L::l. Ei entre los abscisses Ei et Ei + 1

L'equation (1) s 1ecrit

(2)

i = n

~ i = 1 J

Ei + 1

hi Qj i

(E)„ dE

On choisit un nombre n d'intervalles en enargie egal au

nombre m de detecteurs. Les integrales &

f Ei+ 1

ifj ( E) • dE = Ei

On obtient alors : i = n

Aj·= ~ hi „ i = 1

(3)

Tij pauvent etre calculees separement.

Tij seit sous forme matricielle :

[A} = [r1 „ Ge@' /

44

Le vecteur solution [ h) est obtenu par inversion de [ T]:

h = T - 1• A

Le resultat 11brut 11 ainsi obtenu est instable vis a vis des erreurs de

mesure et presente des Valeurs negativas. Une methode iterative, ex-

posee dans la reference /4/ permet de regulariser lc resultat.

Cette methode de regularisation procede par minimisation

d 1 une forma quadratique representant la norme de (hJ . On admet que

la representation ayant la forme la moins complexe est physiquament

la meillaure. La convargence est obtenue par des Variations sur las

observables Aj. Ces Variations r3stent acceptables tant qu'elles

n•excedent pas les erreurs de mesure commises sur les Aj. Le resul

tat final, qui est donc obtenu a partir de compensations antre des

erreurs de mesure, est cense ßtre connu dans la limitc das incerti

tudes sur les reponse~ spectrales (jj (E). (erreur de 11 justesse 11 du

systeme spectrometrique).

Translation:

~he computational progra.mme employs the matrix inversion method.

We have an ordered series of m detectors identified by the subscript

j and with a known spectral response crj(E). Let ~(E) be the spectrum

sought; it must be zero outside the lower (Em) and upper (~) energy

limits. The observable Aj of the detector of rank j (induced a.ctivity) is given by

1 ~ (E) • cP (E) • dE

Em J

AJ =

We represent ~(E) by a constant ordinate hi over an interval 6Ei

between the abscissae Ei and Ei + 1„

Equa.tion (1) is written as follows:

A· = J

i = n ~ L-

i = 1 (

Ei+

hi Oj (E)„ dE

JEi

(1)

(2)

45

We choose a number n of energy intervals equal to the number of

J Ei+ l detectors m„ The integrals o.(E).d.E = Tij can be calculated

Ei J separately„

i „ n We then obtain A. = ~ hi.Tij or0 in matrix form,

J i "' 1

[r 1 "

The solution vector [h] is obtained by inversion of[TJ

h "' T-1.A

The "uncorrected" resul t obtained in this wa:y is unstable wi th respect

to measurement errors and has negative values. By means of an iterative

method (described in Ref •. /4/) it is possible to correct the result.

( 3)

This correction method is based on minimization of a quadratic form

representing the norm of Lh]. It is assumed that the representation having

the least complex form is physically the best. Convergence is achieved by

variations in the observables A .• J

These variations are acceptable as long

as they do not exceed the errors involved in measuring the observables Aj•

The final result, which is accordingly obtained from compensations between

mea.surement errors, is considered to be known within the limit of the

uncertainties associated wi. th the spectral responses oj(E) - "precision"

error of the spectrometric system.

SPECTRA PROCESSED: I. Spectrum ( 1 result, Fig. 17 and 18)

II. Spectrum ( 1 result, Fig. 19 and 20)

REPRESENTATION MODE OF THE RESULTS: 37-group spectra

ENERGY REGION: 10-9 - 20. MeV

GUESS SPECTRUM LIBRARY: No

REMARKS: The thermal and epithermal neutrons are represented

only by 1 group below 0.5 MeV

46

0 2 4 6 8 10 1 2 1 4 16 18

1011 1011

> w ::L --..... LJ 1 0 10 w (/)

--..... N

* * 109 109

::L LJ --..... z

z 108

108

X ::::J _J

LL 10

7 10

7

_J S32(NPlP32 0: FE54(NPlMN54

Nl58(NPlC058 1--z TH232(NFJf,p,

106 w U238(NFJf,p, 106

0:::: IN115(NNlIN115M w LL NP237(NFJf,p,

LL U235(NFJf,p,

0 10

5 1 0

5

0 2 4 6 8 1 0 12 14 16 18

ENERGY IN MEV


0 ,5 - 1 .o 0. 426 o.5 2.088E+10

1 • 0 - 1 ,5 o.875 1 .o 1 .755E+10

1 • 5 - 2.0 1 .088 1 ,5 1 .370E+10

2 .o - 3.0 1. J 60 2.0 1 .023E+10

3 .o - 4,5 1 .038 3,0 5.025E+09

4 ,5 - 6.0 o.675 4,5 1.411E+09

6 .o - 8.0 1 .103 6.0 6.042E+08

9.0-10.0 0.521 8.0 1 .002E+08

10.0-14.0 1 .145 10. 0 4.965E+07

14.0-18.0 1 • 572 14. 0 2 .150E+06

CHARACTERISTIC INTEGRALS AVERAGED ACTIVITY DEVIAT!ONS

11 12 [ 3 !4 l 5 l s A1 Az A3 A4

ORIGINAL 0. J 57 0.222 3. IOE+4 0. 140 0. 131 8.45E+4 18.33% 7.92% 9.so% 6°92%

FEW-GR. o.089 0. J 98 1 .53E+4 o.040 0. 116 4.4BE+4

MR. RUXEROLLF. FRANCF.

FIG. ~ 7

1 o-10 i o-9 10-8 10-7 10-6 i o-5 10-4 10-3 i 0-2 10-1 10° 101 10 2

1011 1011 ~

> w L

" u 10 1~ / \, +1010 w

(/)

" N

* * L u

109+ 1 / ~ +io

9

" z -

bj z H ,„ ~ . "J \ t10' X 108

::J CD _J .f>.

LL .....:i

_J CU63CN2NJCU62 a:: 1127CN2Nlll26 ~

107 RL27CNHElNR24 01 +107

f-MG24CNPJNR24 z D

w FE56CNPJMN56 D n::: S32CNPJP32 [=:J w

FE54CNPlMN54 c:::=i LL LL Nl58CNPJC058 c:::=i ~

10 6 TH232CNFJF.P. c::::=J i +ios 0 U238CNFJF.P. C:=::J INllSCNNl!Nl!SM c::::=J

NP237CNFJf.P. c::::==:J U235CNFJf .P.

105

1 !

1 1 1 1 1 1 1 1 1 1 111 1 1 0

5

1 o-10 i o-9 i o-8 1 o-7 1 o-s 1 0-5 10-4 10-3 1 0-2 10-1 1 0° 101 1 02

ENERGY IN MEV

MR. BUXEROLLE. FRRNCE.

> w L: '-. LJ w (f)

'-. N

* * L: LJ '-. z

z

X :::::> _J

LL.

_J

a:

rz w a::: w LL. LL.

D

48

0 2 4 6 8 10 12 14 16 18 10 9·-;-~-1-~+-~1---+~-1-~-<-~+----l~-+~-+-~-1-~1----1.~...J...~.J...~.L-.......J~-l-10 9

10 6 c:::::::J 1127!N2Nll126

~---~ AL27( NHE lNA24

<--:...---~ MG24!NPlNA24 C:::!:===:=t=~;;;;;;;;i_f_F ES.§5 6 ( NP l MN 5 6

~-----------.1 lP32

4 ( lMN5

'------------' Nl58(NPlCO ~------' TH232( NF JF ,p. '------~ U238! NF lF ,p.

.__ ___ ___, IN115!NNllN115M

~---~ NP237! NF lF ,p. ~------' U235! NF lF ,p.

10 4-+-~-+-~+-~+---+~-+-~-<-~+--"'e---+~-+-~...._~+----+~~~-1-~-1--~1----4---10•

0 2 4 6 8 10 12 14 16 18

ENERGY GROUP

0.5- t.O 1 .o - 1. 5 1 • 5 - 2. 0 2.0 - 3.0 3.0- 4,5 4.5- 5.0 6.o- 8.o 8.0-10.0

10.0-14.0 14.0-18.0

FLUX/REF. FLUX

0.449 1 . 210 1 • 289 1 .176 0.332 1 • 124 0. 466 1 • 912 0.532 1 • 980

CHARACTERISTIC INTEGRALS

ENERGY

o.5 1 .o 1 ,5 2.0 3.0 4,5 6.0 8.o

10.0 14. 0

ENERGY IN MEV

INTEGRAL FLUX

2 .17DE+08 1 .605E+08 8.948E+07 5.038E+07 1 • 368E +07 7.703E+06 1 • 583E +06 8.835E+D5 1.195E+D5 2.390E+04

AVERAGEO ACTIVITY DEVIATIONS

ORIGINAL o.674 o.293 Q.886 o.660 0.235 o.843 47.02% 14.72% 17.56% 11.20%

FEW-GR. 0.334 0.245 o.858 0.260 0.193 o.782

MR. BUXEROLLE, FRRNCE.

FIG. 19

1 o-10 1 0-9 10-8 1 0-1 1 o-6 1 0-5 1 o-4 1 0-3 1 0-2 10-1 10° 101 102

10121 1 1 1 1 1 1 1 1 1 1 1 1 1012 -> w :L "--

10 11+-- /\ +io11 u w (f)

"--N llE llE 1 0

1.llf- ~ 1 FV ~ +io10

:L "'-u "--z -z 109t / ~( ~ t109 ........ c (j'\

'<t ("\J X ::J _J

108+ / r4. +10

8 C?

LL i--1

"""' _J

er: ........ 1-z w lOI FE56CNPlMN56 l'rP +io

1

0::: S32CNPlP32 w LL FE54CNPlMN54 LL N!58CNPlC058 ........ TH232CNFlF.f. D 106 ci~\ +ios U238CNFlF.f.

IN1!5(NNl!N!!5M c:::::J NP237(NFlF.f. c:=:::J

U235CNFlF.f. c:=:=:J

10

5

' 1 1 1

1 10 5 1

i o-10 1 0-9 10-8 1 0-1 1 o-6 1 o-5 1 0 -4 1 o-3 10-2 1 0-1 10° 101 102

ENERGY IN MEV

MR. BUXEROLLE. FRRNCE.

V. CUCULEANU111

D. MOOIOIU

IFNT BUOHAREST, ROMANIA

METHOD:

50

Two methods, differing one from another by the manner of approximating the unknown spectrum ~ (E), underly our programme:

1. The first one is tile method of orthogonal polynominals

consisting in usin6 following expansion /6,7,8/ : rl- {

C'tl(e); (fCE)::: Wle) z: CK-t;1<-(€) 't' Jl.~c

The coe:fficients {ck3 are simply determined by solv:i.ng

the system: .()0

i = 1, 00090GO& N

bµ,.:,"' j WteJO'..·if) &14C~)of.E e~~

·th Ai = L detector sctivity

N = number of de tec tor·s

~· -jth . . v... = ~ re~ction cross-sect1on

Epi = ith reHction threshold

2. The SEcond one is R.D.M.M. method worked out by G. Di

Cola end A. Rota /5/. " 0 775 1 For both methods 1 and 2 , W (E) = e-ß and W(E)= ke- ·

0f were chosen as weighting functions. Lil.gtlerre polynomials were

nsed as lQk(E)} •

SPECTRA PROOESSED: Ie Spectrum ( 14 results ) ; IIe Spectru.m: Not.

1"' RDMM Method 111 3 terms, W(E) = ke-0.775E\[E; ( Fig„ 21) 2, RDMM method, 4 terms, " ( Fig„ 22) 3e RDMM method, 5 terms, lt ( Fig„ 23) 4. Polynom method, 3 terms, W(E)' -= ke -0 „ 775E fE ( Fige 24) 5. ,, 4 terms

111 II ( Fig„ 25)

51

6@ Polynom method, 5 terms, ~(E) 3 ke-0@775ElfE; ( Fig„ 26) 7@ RDMM method, 3 terms, W(E) = e-E ( Fig@ 27) s. Polynom method, 3 terms, W(E) = e-E ( Fig@ 28) 9„ RDMM method, 3 terms, W(E) = e-E ( Fig„ 29)

1 o. RDMM method, 4 terms, W(E) = e-E ( Fig„ 30) 11 EI Polynom method, 3 terms, W(E) = e -E ( Fig„ 31 ) 12„ RDMM Mehtod, 3 terms, W(E) ~ ke-0.775EfE ( Fig„ 32) 13. RDMM method, 4 terms, W(E) = ke-0„7?5E.IB ( Fig„ 33) 14. Polynom method, 3 terms, W(E) = ke-0„7?5EVE. ( Fig„ 34)

REPRESENTATION MODE OF THE RESUL~: 100-group spectra wlith O „ 1 MeV group width@

ENERGY REGION: 0 0 1 - 10 MeV.

GUESS SPECTRUM LIBRARY: No REMARKS: The best results have been obtained using the RDMM method with 3 terms. The more the number of terms, the wors~ the results are. By the polynom method reasonable reaults were obtained only using 3 detectors. By introducing the 4-th and 5-th detectors oscillations occur. This faot points ou~ the inoompatibility of the used cross-section set~

52

0 2 4 6 8 1 0 12 1 4 16 18

101 1 Ü II

> w :E ........

101 u 1010

w (f) ........ N llE llE

109

109

:E u ........ z

z 108 1 ÜB

X ::::> _J

LL 10

7 1 0

7

_J

a:

f-z G241NPlNA24

1 06

1 06 w L27!NHElNA24

a::: AL27 NPlHG27 w LL S321NPlP32 LL IN! 151 NN l IN115H

0 106 106

0 2 4 6 8 1 0 12 1 4 16 18

ENERGY 1 N MEV


0. 5 - 1 .o Q.996 o.s 2°875E+10 1 . 0 - 1 ,5 1. 418 1 .o 2.Q95E+10 1 . 5 - 2.0 1. 433 1 ,5 1 .471E+10 2. 0 - 3,Q 1. J 98 2.0 1 .o ! SE+ 10 3 .o - 4,5 0.912 3,Q 4 .767E+09 4 ,5 - 6.0 0.853 4,5 1 .592E+09 6 .o - 8.o 0.948 6°0 5.7J7E+08 8.0-10.0 1 . 409 9.0 1 .386E+08

10.0-14.0 0.046 10.0 1 .904E+06 14.0- J8.0 14 .o

CHARACTER 1ST1 C INTEGRALS AVERAGEO ACTIVITY DEVIATIONS

11 12 13 1 4 15 16 A1 A2 A3 R4

ORIGINAL 0 .077 o.069 0.075 0.097 20.90% 8.52% 8.52%

FEW-GR. 0.063 o.054 o.060 o.082

MR. CUCULERNU, RGMRNIR. SPECTRUM ~ ~ ~ •

FIG. 21

53

0 2 4 6 8 10 12 1 4 16 1 8

101 -1011

> w l:

' 101 1010 u

w (/)

' N )!(

* 109

109

l: u

' z

z 1 0 B 1 0 8

X :::J _J

LL 10

7 10

7

_J

a:

f-z L27CNHElNA24

106

106 w G24CNPJNA24

et::: A 27CNPJMG27 w LL S32CNPJP3 LL IN115CNNlIN115M

0 1 0

5 10

5

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0 ,5 - 1 .o o.542 o.5 2.391E+10 1 .o - 1 ,5 1 .078 1 .o 1 .966E+10 J.5 - 2.0 1. 340 1 ,5 1 .492E+l0 2 .o - 3.0 1 .311 2.0 1 .065E+10 3 .o - 4,5 1 .o 13 3,0 4.762E+09 4. 5 - 6.0 o.665 4,5 1 ·235E+09 6 .o - 8.o 0 ,543 6.0 4.403E+08 9.0-10.0 1 .936 8.o 1 • 922E+08

10.0-14.0 0 .104 10.0 4.336E+06 14.0-18.0 14 .o

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVITY OEVIATIONS

l 1 12 1 3 1 4 15 I s A1 A2 A3 A4

ORIGINAL 0 .469 0 .175 0 ,723 o.085 21 .19% 9 .18% 9 .18%

FEW-GR. 0.274 0 .144 o.350 o.084

MR. CUCULERNU. ROMRNJR. SrECTRUM • ~ 2 ~ •

FIG. 22

54

0 2 4 6 8 10 1 2 1 4 16 18

101 1011

> LLJ :E .......

101 1010 u

LLJ (j) ....... N

* llE 10

9 10

9 :E u ....... z

z 1 0° 106

X ::J _J

LL. 1 07

107

_J

a: 1-z L27!NHElNA24

106

106

LLJ G24!NPlNA24 0::: A 27!NPlMG27 LLJ LL. S32!NPlP 2 LL. JNl 15! NN l IN115H

D 105

105

0 2 4 6 8 1 0 12 1 4 16 18

ENERGY IN MEV


0. 5 - 1 .o o.5 7.878E+09 1. 0 - 1 ,5 Q.024 1 .o 1.584E+10 1 ,5 - 2.0 1 .122 1 ,5 1 .574E+10 2 .o - 3.0 1 ,533 2.0 1 . 217E + 10 3 .o - 4 ,5 1 .183 3,0 4.835E+09 4 ,5 - s.o 0°309 4,5 7 .173E+08 6 .o - 8.o Q.288 6.0 3.476E+08 8.o - 10.0 2 .193 8.o 2. l 62E+08

10.0-14.0 Q.081 10.0 3.374E+06 14.0-18.0 14 .o

CHARACTERJST!C INTEGRALS AVERAGED ACTIVJTY OEVIATJONS

11 12 l 3 14 15 16 Al A2 A3 A4

ORIGINAL 0.935 2.744 o.934 1 .968 27.53% 11. 40% 11. 40%

FEW-GR. 0.794 2.585 o.715 1. 230

MR. CUCULERNU. ROMRNJR. SPECTRUM * * 3 * *

FIG. 2~

55

0 2 4 6 8 10 12 14 16 18

101 1 Ü II

> w l:

' 101 u 1010

w (f)

' N )IE )IE

1 09

109

l: u

' z

z 10° 1 ÜB

X ::> __J

LL 1 07

107

__J

cc 1-z

1 06 106 w

Cl::: AL271 PIMG27 w LL S32!NPIP32 LL INl 151NN1 IN115M

D 10

5 1 06

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o o.893 o.5 2·737E+10 1 . 0 - 1 ,5 1 . 307 1 .o 2.037E+10 1 . 5 - 2.0 1. 363 1 ,5 l .463E+10 2 .o - 3,0 1 .187 2.0 1 .029E+10 3 .o - 4,5 o.953 3,0 4.957E+09 4 ,5 - 6.0 o.913 4,5 1 ·638E+09 6 .o - 0.0 0.945 6.0 5.474E+08 0.0-10.0 1 .181 0.0 l.160E+08

10.0-14.0 0.035 10.0 1 .435E+06 14.0-18.0 14 .o

CHARACTERISTIC INTEGRALS AVERAGED ACTJVITY DEVIATIONS

I 1 I 2 I 3 1 4 I 5 I 6 A1 A2 A3 A4

ORIGINAL 0.031 o.056 0.020 0.064 21 .98% 9 .18% 9 .18%

FEW-GR, 0.025 0.040 0.022 0.055


FIG. 24

56

0 2 4 6 8 10 1 2 1 4 1 6 18

101 1 Ü II

> w :c .......

101 1010 u

w (f)

....... N l!E )!(

109 10

9

:c u ....... z

z 1 08 10

8

X :::) _J

LL 107 10

7

_J

a: f-z

1 06 10

6 w c::=::::J AL 2 7 ( N ElNA24 a:::: AL27( PlMG27 w LL S32(NPl 32 LL IN 115 ( NN l IN 1 !SM

0 105 10

6

0 2 4 6 8 10 12 1 4 16 1 8

ENERGY IN MEV


0 ,5 - 1 .o 2.296 o.s 4.231E+IO 1 .o - 1 ,5 2.365 1 .o 2.433E+IO 1 ,5 - 2.0 1 .647 1 ,5 1 .392E+IO 2 .o - 3.0 o.837 2.0 8.682E+09 3 .o - 4,5 o.633 3,0 4.923E+09 4 ,5 - 6.0 1. 470 4,5 2.7!8E+09 6 .o - 0.0 2 .193 6.0 9.607E+08 0.0 - 10.0 0.0

10.0-14.0 10.0 14.0-18.0 14. 0


I 1 I 2 I 3 I 4 I 5 ls A1 Az AJ A4

ORIGINAL 2 .148 I ,372 4,949 1 .256 31 .90% 24.48% 2 4. 4 8%

FEW-GR. Q.959 1 .368 1 .005 1 .213

MR. CUCULEANU, ROMANIA. SPECTRUM * ~ 5 * *

FIG. 25

57

0 2 4 6 8 10 12 1 4 16 18

i 01 1 0 II

> w L

~ ' 10 1 1010 u

w (/)

' N llE llE

1 09

109

L u

' z

z 1 0 B 109

X :::::> _J

LL 10

7 10

7

_J

a:

r-z L271NHElNA24

1 06

106 w G241NPlNA24

0::: A 271NPlMG27 w LL S321NPlP 2 LL JNl 151 NN l JNl 15M

D 10

6 10

5

0 2 4 6 8 10 12 1 4 16 18

ENERGY IN MEV


0 ,5 - 1 .o 0.5 7.886E+09 1 .o - 1 ,5 Q.024 1 .o 1.584E+IO 1 ,5 - 2.0 1 .122 1 .5 1 .574E+IO

2 .o - 3.0 1 .633 2.0 1 • 2l7E+10

3 .o - 4,5 t.183 3.0 4.835E+09 4 ,5 - 6.0 0.309 4,5 7 .171E+08

6 .o - 0.0 0.200 6.Q 3 .478E+08

0.0-10.0 2 °196 0.0 2. l 65E+08

10.0-14.0 0.001 10.0 3.374E+06

14.0-18.0 14 .o

CHARACTERJSTJC INTEGRALS AVERAGEO ACTIVJTY DEVIATJONS

11 12 1 3 I 4 I 5 I s A1 A2 A3 A4

ORIGINAL Q.938 2.742 Q.940 1 .963 27.54% 11 .44% 11. 44%

FEW-GR. Q.796 2.582 Q.718 1. 228

MR. CUCULEANU. ROMANIA. SPECTRUM * * 6 * *

FIG. 26

58

0 2 4 6 8 10 12 14 16 18

1 0 l 1011

> w :c

' 101 1010 u

w (/)

' N )«

* 109 10

9

:c u

' z

z 1 08 1 0 B

X ::J _J lJ_

107 10

7

_J

cr:

1-z M 24CNPlNA24

106 1 0

6 w A 27CNHElNA24 0:::: ' AL27! PlMG27 w S32CNPlP32 lJ_ lJ_ 1N115CNNl1N1l5M

0 106 10

5

0 2 4 6 8 1 0 1 2 14 1 6 18

ENERGY IN MEV

ENERGY GROUP FLUX/REF, FLUX ENERGY INTEGRAL FLUX

0 ,5 - l .o 2' 133 o.5 4.033E+JO l .o - l ,5 2' 120 l .o 2.362E+l0 1 ,5 - 2.0 l ,579 l '5 1.429E+10 2 .o - 3,0 l '144 2.0 8.945E+09 3 .o - 4,5 o.750 3.0 3.806E+09 4 ,5 - s.o o.680 4,5 1 . 194E+09 6 .o - 8.o o.680 6.0 3.809E+08 e.o - 10.0 o.715 8.o 7.009E+07

10.0-14.0 0°017 10 .o 7. 176E+05 14.0-18.0 14 '0

CHARACTERJSTIC INTEGRALS AVERAGED ACTIVITY DEVIATlONS

11 12 13 1 4 l 5 16 A1 Az A3 R4

ORIGINAL 0.236 l .037 0' 160 o.787 39.01% 33.72% 3 3 '72%

FEW-GR, 0.225 l .027 0' 151 o.794

MR. CUCULERNLJ, ROMRNJR. SPECTRUM * * 7 * *

FIG. 27

59

0 2 4 6 8 10 1 2 1 4 16 18 1011 1 0 II

> w :L

' 1010 1010 u w (f)

' N

* * 1 0

9' 10

9 :L u

' z

z 1 0 e 1 0 e

X ::::> _J

LL 10

7 10

7

_J

cr: f-z

jl 06 10

6 w Q::'. AL27CNPlMG 7 w S32CNPlP32 LL LL IN115CNNlIN115M

0 105 10

5

0 2 4 6 8 10 1 2 1 4 16 18

ENERGY 1 N MEV


0 ,5 - 1 .o 0.222 o.s 2.051E+10 1 .o - 1 ,5 0°909 1 .o 1 .877E+IO 1 . 5 - 2.0 1 .268 1 ,5 1.477E+10 2 .o - 3.0 1 °288 2.0 1 .074E+10 3 .o - 4,5 1 .058 3,0 4.952E+09 4. 5 - 6.0 Q.833 4,5 1 .270E+09 6 .o - 8.0 o.544 6.0 2.743E+08 8.0-10.0 0.263 8.Q 2.561E+07

10.0-14.0 10.0 1.191E+05 14 .o - 18.0 14. 0

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVITY DEVIATIONS

11 I 2 13 14 I s 1 6 A1 A2 A3 A4

ORIGINAL Q.233 Q.431 0°067 Q.080 33.86% 15.36% 15°36%

FEW-GR. Q.208 Q.369 0°057 Q.085

MR. CUCULERNU. ROMRN!R. SPECTRUM * * 8 * *

FIG. 26

60

0 2 4 6 8 10 12 14 16 18 10 1 1 0 II

> w l'.: .......

10 1 u 1010 w (f)

....... N

* * 10° 10 9 l'.: u ....... :z

:z 108 1 0 8 -X ::::> -' LI.. 10 7 10 7

-' a: 1-:z FE 6!NPlMN56 w 10 6 532lNPlP32 1 0 6

a::: Nl56!NPJC05 w LI.. IN! 15( NN l IN! 15M LI.. NP237!Nf)f,p,

Cl 10 6 10 6

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0 .5 - 1 .o 1.270 0.5 2.763E+IO 1 .o - 1.5 1.269 1.0 1.766E+IO 1 .5 - 2.0 1 .065 1.5 1 .2IOE+10 2 .o - 3.0 0.005 2.0 6.649E+09 3 .o - 4,5 0.817 3.0 4.671E+09 4 .5 - 6.0 0.909 4,5 1 .626E+09 6 .o - e.o 1 .137 s.o 6.43BE+OB 0.0-10.0 1 .266 0.0 1.243E+08

10 .o - 14 .o 0.031 10.0 1.296E+06 14.0-IB.O 14.0

CHARACTERISTIC INTEGRALS AVERAGED ACTIVITY OEVIATIONS

11 12 l 3 14 l s 15 A1 A2 A3 A4

ORIGINAL 0.040 0.062 0.035 0.061 19.58% B.87% e.cn

FEW-GR. 0.034 0.059 0.029 Q.058

MR. CUCULEANU, ROMANIA. SPECTRUM m m 9 m m

FIG. 29

61

0 2 4 6 8 10 1 2 14 1 6 18

1 01 1011

> w ::c

' 10 1 u 1010 w ({)

' N )!!

)!! 1 0 9 1 0

9 ::c u

' z

z 10 6 1 0

8

X :::::> _J

LL. 10

7 10

7

_J

a: 1-z F 56(NPlMN56

1 06

1 06 w S32(NPJP3

a::: NI58(NPlC 58 w LL. INl 15( NN l IN! !SM LL. NP237(NFlf ,p,

0 10

6 1 0 5

0 2 4 6 8 10 1 2 14 1 6 18

ENERGY IN MEV


0 ,5 - 1 .o Q.879 0.5 2.681E+IO 1 .o - 1 ,5 1 • 409 1 .Q J .992E+IO 1 ,5 - 2.0 1. 427 1 ,5 1 .372E+IO 2 .o - 3,0 !.114 2.0 9. !80E+09 3 .o - 4,5 0.755 3.0 4.!76E+09 4. 5 - 6.0 0.755 4.5 1 .548E+09 6 .o - 8.o 1 .052 6.0 6 .457E+08 8.o - 10.0 1 .681 8.o 1 .652E+08

10.0-14.0 0.051 10 .o 2. t03E+06 14.0-18.0 14 .o

CHRRRCTERISTIC INTEGRALS RVERRGEO RCTIVITY DEVIRTIONS

I1 I 2 I 3 1 4 15 I 6 A1 Az R3 R4

ORIGINAL 0. !63 o.088 0 .11 s 0.094 22.23% 10.09% !O.J9%

FEW-GR. 0 .138 o.060 o.096 0.075

MR. CUCULEANU, ROMANIA. SPECTRUM * * 10 * *

FIG. ~O

62

0 2 4 6 8 10 12 1 4 16 18

101 1011

> w l::

' 101 u 1010

w Cf)

' N

* * 1 0 9 10

9 l:: u

' z

z 10° 108

>< :::> _J

LL. 107

1 07

_J

a:

1-z

1 06

1 06 w

n::: Nl58CNPlC058 w LL. !NI 15( NN l !NI 15M LL. NP237CNFlf,p,

C) 10

5 10

6

0 2 4 6 8 10 12 1 4 16 18

ENERGY 1 N MEV


0 ,5 - 1 .Q o.969 o.5 2.682E+IO 1 .o - 1 ,5 1 . 327 1 .o J .923E+IO 1 ,5 - 2.0 1 . 342 1 ,5 J.340E+IO 2 .o - 3,0 1 .133 2.0 9. J 27E+09 3 .o - 4,5 0.844 3,0 4.039E+09 4 ,5 - 6.0 o.688 4,5 1. JOIE+09 6 .o - 8.o o.527 5.0 2.787E+08 0.0 - 10.0 o.386 8.o 3.776E+07

10.0 - 14.0 10 .o 3.!IOE+05 14.0-18.0 14 .o


I 1 I 2 I 3 l 4 I 5 15 A1 R2 A3 A~

ORIGINAL 0. J 78 o.046 o.067 0.056 38.33% 11 °99% 11 .'19%

FEW-GR. 0. J 59 0.035 0.059 o.043


FIG. 31

63

0 2 4 6 8 10 1 2 14 16 18 10 1 10 II

> w l::

' 10 1 1010 u w (/)

' N )j! )j! 10 9

1 0 9 l:: u

' z

z 10 8 1 0 8

X :::) _J

LL 10 7 10 7

_J

a: ,_. f-z F 56!NPlMN56

1 0 6 1 0 6 w S32lNPlP3 a::: Nl58lNPlC 58 w !NI 15( NN l !NI !SM LL LL NP237lNFlf,p,

D 1 0 5 1 0 6

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0 ,5 - 1 .o 0.992 o.s 2.729E+IO 1 .o - 1 ,5 1 .376 1 .o 1 .952E+IO 1 ,5 - 2.0 1. 350 1 ,5 1 .347E+IO 2 .o - 3,0 1 .o8s 2.0 9. J69E+09 3 .o - 4 ,5 o.789 3.0 4.295E+09 4 ,5 - 6.0 o.763 4 ,5 1 .546E+09 6 .o - 8.o 0.997 6.0 6.345E+08 8.0-10.0 1 .817 8.o 1 .789E+08

10.0-14.0 0.064 10.0 2.661E+06 14.0-18.0 14 .o


I 1 I 2 I 3 I 4 l 5 l 5 A1 A2 A3 A4

ORIGINAL 0.214 o.054 0 .131 0.065 22.21% 9 ,771: 9. :n

FEW-GR. 0 .171 0.040 0 .106 o.oso

MR. CUCULERNU. ROMANIA. SPECTRUM m m 12 m m

FIG. 32

64

0 2 4 6 8 1 0 12 14 16 1 8

101 1011

> w l::

' 101 1010 LJ

w ())

' N

* * 109

l:: LJ

' z

z 106 10

8

X ::J _J

LL 107 10

7

_J

CI E56CNPlMN56

1-z Nl58CNP C058 w 1 0

6 IN115CNNllN115M 1 06

Cl::: NP237CNFlF.P. w NP237CNFlF.P. LL LL

0 106 10

6

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o 0.863 0.5 2.657E+10 1 .o - 1 ,5 1. 320 1 .o 1.981E+10 1 . 5 - 2.0 1 .400 1 ,5 1 . 400E + 10 2 .o - 3,0 1 .188 2.0 9.543E+09 3 .o - 4,5 o.826 3,0 4.207E+09 4 ,5 - 6.0 o.620 4,5 1 .330E+09 6 .o - 0.0 0.788 6.0 5.895E+OB 0.0 - 10.0 2.322 0.0 2. 298E +08

10.0-14.0 0 .107 10.0 4.440E+06 14.0-18.0 14 .o

CHARACTERISTJC INTEGRALS AVERAGED ACTJVJTY DEVIATIONS

l 1 l 2 13 1 4 l 5 l s A1 A2 A3 A4

ORIGINAL o.618 o.069 0 .107 0.060 24.93% 8 .72% 0. 72%

FEW-GR. 0.424 0.050 0.009 o.048


FIG. 33

65

0 2 4 6 8 1 0 1 2 1 4 1 6 18 10

1 1 0 II

> w E

' 101 1010 u

w (/)

' N ll( ll(

1 09 l 0

9 E u

' z

z 108 1 0 °

>< ::::> _J

LL 1 o' 1 o'

_J

a: 1-z

1 06 1 0

6 w Cl:'. NI58CNPJC058 w LL INl 15C NN l INl 15M LL NP237CNFJF.P.

0 10

6 1 06

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0 .5 - 1 .o o.963 o.5 2.708E+IO 1 • 0 - 1 ,5 1 .369 1 .o 1 .954E+IO 1 ,5 - 2.0 1 . 378 1 ,5 J.352E+IO 2. 0 - 3.0 1 .137 2.0 9 .131E+09 3. 0 - 4,5 o.821 3.0 4 .024E+09 4. 5 - 6.0 Q.677 4 ,5 1. l 65E+09 6 .Q - 8.o Q.615 6.0 3.560E+08 8.0-10.0 o.762 8.o 7.490E+07

10.0-14.0 0.024 10 .o 9.817E+05 14.0-18.0 14 .o


I 1 I 2 I 3 I 4 I 5 I 6 A1 Az A3 A4

ORIGINAL o.087 o.058 o.076 Q.070 34.06% 12. 43% 12. ~ 3%

FEW-GR. o.081 Q.043 Q.066 0.055

MR. CUCULERNU, ROMRNJR. SPECTRUM ~ ~ 14 ~ ~

FIG. 34

66

A. HRABOVCOVA

INSTITUTE OF INDUSTRIAL HYGIENE, BRATISLAVA, CZECHOSLOVAKIA

METHOD:

For the evoluation cf f3st neutron spectra frc:o incuced

activities of threshcld and fis~ion ~ete~ctcrs we use the rnethGd

P.D:.'1~ given by DiCola and :Rcta [5! „ Thn unl:r:.C;wn diffe:-ential f'l~x

densti t;y :f\:nctior. is ap.!_)roxi:n.;;iteC. by a sy8terr. of orthonoral f'..lr"-

ctio~s. We use two systerns

1. the sy s tem l 1n /EI l 1 l / 'E/ n = e

E 2

is the n-th l;agserr pclyno!:i::.ol /the p3rEime ter ol.. = C/ U/2)

2. the system Ln / p0E/ • togethe1~ wi th a v:e~t;hting functicn

w/E/ = 0. 77 \[E · -0.7-,6 E e .. , (1;2) Ln /()0E/ ure al.so Laguerr polynomials, f(;= O. 776 and paran1 eter

J. = ~ L2,3] .

SPECTRA PROCESSED: I. Spectrum ( 1 result, Fig. 35. ) II. Spectrum ( 1 result, Fig. 36. )

REPRESENTATION MODE OF THE RESULTS: 55-point differential

speotrum.

ENERGY REGION: 0 0 2 - 11.0 MeV

GUESS SPECTRUM LIBRARY: No

REMARKS: Originally, more results have been oaloulated, but only the best results were sent in tabulated form. Other results could not be taken into account, since they were sent to us in graphical form only.

67

0 2 4 6 8 10 1 2 1 4 16 18

101 1 o11

> w ::E

' 101 u 1010

w (/')

' N

* * 109

1 09

::E u

' z

z 1 OB 1 OB

X ::i _J

lL 1 0

7 10

7

_J MG 4!N NR24 ([ R 27!NH NR24

RL27!NP lMG27 1--z

1 06

S32!NPlP32 w NJ58!NPlC058 1 0

6

0::: TH232!NF)f,p, w 1N115 ( NN l 1N115M lL lL NP237tNFJf,p,

0 1 05 1 0

5

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8

ENERGY IN MEV


0 '5 - 1 .o 0°840 0.5 2.534E+l0 1'0 - l ,5 1 '217 1 .o 1 .876E+10 1 '5 - 2.0 1 '249 1 ,5 1.341E+10 2 .o - 3,0 l .074 2.0 9.430E+09 3 '0 - 4,5 0.858 3.0 4.607E+09 4 '5 - 6.0 0.849 4,5 1 .621E+09 6 .o - 8.o o.966 6.0 6.065E+08 8.0-10.0 1 '392 8.o 1 .653E+08

10.0-14.0 o.729 10 '0 3.024E+07 14.0-18.0 14 '0

CHRRRCTERJSTJC INTEGRRLS RVERRGEO RCTlVITY OEVJRTJONS

11 12 l 3 1 4 15 15 R1 R2 R3 R4

ORJGJNRL o.058 0.046 0.048 0.040 17' 19% 8.44% 8.44%

FEW-GR. 0 .047 0°031 0.039 0.032

MR5. HRRBOVCOVR. BRRTl5LRVR

F:::G • 35

68

0 2 4 6 8 1 0 1 2 1 4 16 1 8 1 0 9 10 9

> w :E

' u w 10 6 1 0 6

(f)

' N )!(

)!(

:E u

1 0 7 1 0 7

' z

z

X 10 6 10 6

:::::> _J

LL.

_J MG24(NPlNA24 a: AL27(NHElNA24

f-1 0 5 S32(NPlP32 10 5

z w Nl58(NPlC058 0:::: TH232(Nf Jf,p, w LL. IN115(NNllN115M LL. NP2371NF)f ,p,

0 10 4 104

0 2 4 6 8 10 1 2 1 4 16 1 8

ENERGY IN MEV


0. 5 - 1 .o o.248 0.5 1 .338E+08 1 . 0 - 1 . 5 0. 458 1 .o 1 .027E+08 1 . 5 - 2.0 0.695 1 . 5 7.581E+07 2 .o - 3,0 o.878 2.0 5.473E+07 3. 0 - 4. 5 1 .016 3,0 2.734E+07 4. 5 - 6°0 1 . 141 4,5 9.041E+06 6. 0 - 8.0 1 .522 6.0 2.828E+06 8.0-10.0 1. 183 8.0 5.413E+05

10.0-14.0 0.381 10. 0 6.854E+04 14.0-18.0 14. 0

CHARACTERISTlC INTEGRALS AVERAGEO ACTIV!TY OEV!ATIONS

11 12 1 3 14 15 l s A1 A2 A3 A4

ORIGINAL 0. 123 0.510 0 .100 0. 400 22. 67% 13. 41 % 13. 41 %

FEW-GR, 0 .119 0.484 0 .108 0. 413

MRS. ~RPBOVCOVR. BRnTISLRVR

FIG. 36

69

o.P. JONEJA, D.v.s. RAMAKRISHNA, M.P. NAVALKAR

BHABHA ATOMIC RESEARCH CENTER, TROMBAY, INDIA

METHODS:

T.lle analyeis ie done with following approximations

ae regarde the neutron epectrum in a reactor

1) Modified fiesion epectrum by both effP.ctive and

threshold concept

2) Polynomial approximation by threshold concept

3) Perturbation approximation by threshold concept

4) Relative deviation minimisation by threshold conoept

In the present paper which ie final we report the

analyaia taking errore on activities end cross-sections.

The method of calculating errore is given in the Appendix.

A brief description of each method is given below:

1) Modified fieaion epectrum

a) Threehold Energy Anälysis 1 Tbie method assumea that

tne neutron epectrum at the eite of intereet in a reactor

can be expreeeed in the form of fieeion epectrum with

modified epectral indice • We aseume that reactor

epectrum ie given by

{ K -J1

-=--

where r is to be evaluatea.

70

The reeponse integral for ~"' deteotor with thie

a1swnption would b• given b1

1:""'~

f i;„ ( 1}1> (-;;) <At=

!! p is choeen euch that it repreeenta the actual

epeotrum then :trom aba>"le expreseion k should be a. conetant

tactor irrespectiye of tne deteotor under coneideration. The

computer code 9PARTDIS0 9 finde the l raotors for each dete

otor for each p 9 then finde the mean valne o:r lt arid then

deviation from t.he mean value end f:lnally average peroentage

deviation from the mean va!uec Mathematically the progra.mme

finda ihe !ollowing

/ ~""~ -P" -

Km • J. ~ ! e_, 6~ l E J o{ l:"

DD III

MDKM MPDm • - 0 x 1 oo

71

ODI f which reaulta iD

T&lu•

Addition eo 'IITEGBJ.L• find• th• integrat•d

in defined bJ ~hreahold

ea :t'rom 'ttle fo l lowing ... '11".„.,,_ s aion

&;,,...

't(t=)j •

!rhe prooedure to1lowed

1ame as in the oaee or threshold energie• ••oept thai

• es the oorrespond 1Dg et.feo"tive Talu•

detinitiora ot ef!eotiTe cro1s•aeotion1

{7~t~) t(t;)d (:,~

lt tne tne

fiaaion torm th different

t:~A#C { 1~r-J "~ Lf) e,.- c.l E ~

72

•nergy is calculat~d for all the deteotora and then the

!ollowiDg e%preseiona oorrelat:lng the effective cross-aeotion

w1th specific activitiee ia made use ot

rtv\t-<j

~ ( G„ lt) e_-ftolt: ~ ol~" ~Ge."' ~i~

f.,._.AA

~- ( \lE .,(h-

'=e n..

o:r

K -btlM

If the (> represents the neutron speotrum at the

eite or interest, then obviouely the K faotor will be eam.e

irreepective of the detector coneidered• therefore we etart

OD the eame lines aa in the case of 'PART DISC' acd evaluate

W?DKM :!or the varioue values or f and select tha.t ß w.nicb givee tne minimum val ue o:r MPDKA. The computer oode

which aooomp!iehes tnie ia 'DISOOVRY'. Tbe values of

10 obtained are fed to a programme 'INTEGRAL• which givea

integrated fluxee in the energy groupa defined by e!fectiYe

threshold energies$

2) POLYNOMIAL APPROXIMATION

The reaotor speotrum in thie oaee ie expressed aa a

polynomial or mth degree in energy. The degree of polynomial

in thie caae ie limited by the n'!J11lber ot detectora available.

In generaJ. if the in:ror:at!on is availabie 1·or n detec:rtor11,

tne maximum degree in energy will be (n-1)th. The reeponee

73

PA-f - - - - - .... tik- « t.

-iJ: h\~

~· J_ Gvw (~)+(,1::)vti; t~""

t"'~ G~~

• ( t\oG..,li;)vl F + [ c.t,f c,.,,(r;. )olG--+ ft;.,_

- - ~

oO

/;(,, wl- f G f1.< l ;;c ) -+ ( G) d ;;: :. . f) r~1-tv.

For n detectora we shall have n euch equatione and

tnerefore n unkcowns wnich oan be founa out either by

matrix inversion or by eubstitution metnod. The computer code

'POLYNOM' finde out the varioue coefficienta by using matrix

1nvers1on eubroutioe. Once the ooefficiente are known 9 then

trom above expression it finde out thc differential !lux at

threshold end effeotive threshold anergies ae well ae

integrated fluxes in the respeotive energy groupa.

.... .

74

ID eeriea expaneion methcd oue IUlflttflletir the speot:ru.m ae

th• product ot a weight function or guess appro%imate tunot1aa

and a Logorre or Legendre polynom1al expaneion such ae

cf {t:-)-; \v(t=-) ~Cl~ '*~(E-) I."- '

ie tne approximate function ~ -E

e. Where W ( E)

Clk are the coeffioienta which are to be

eva.iuated by the oalouJ.ationa

't-n (G) ie the set of arbi tary function

At > _{°1)0,(F)qi(~)vlir = • (c-. (;;) w(0) ~ tt 1-c 'f' Kl~ )d &

() VI k ::... 1 ::: 2' 4K Sek ~~ lt the number of deteotore are eame aa cumber o! terms

-t

[Ai] ~ [ ~ 1 [~ 1 \.oh~t. $ i K '&. j 6(i:-) IAJ lt=-) '+' K (f ) In the min1m1sation

&D4 flwt ctrum 111 given by df CE) for which "ie 11inimwa„

75

SPECTRA PROCESSED: I 0 Spectrum ( 5 results ) II„ Spectrum ( 5 results )

I. 1„ PAR~TIISC method; ( Fig. 37 ) 2„ DISCOVRY method; ( Fig 0 38 ) 3. POLYNOM method; ( Fig 0 39 ) 4„ PERTURB method; ( Fig 0 40 ) 5o RDMM method. ( Fig„ 41 )

II. 1„ PARTDISC method; ( Fig. 42 )

2. DISCOVRY method; ( Fig 0 43 )

3. POLYNOM method ( Fig. 44 ) ~. PERTURB metho J; ( Fig 45. ) 5. RDMM method. ( Fig. 46 )

REPRESENTATION MODE OF THE RESULTS: a) For PARTDISC and DISCOVRY results: 40-pcdnt differen

tial spectra b) For POLYNOM and PERTURB methods: 11-group ( for the I.

Spectrum ) and 9-group ( for the II. Spectrum ) step fluxes„

c) For the RDMM method: 27-point differential spectrum. ENERGY REGION: o„o - 20.0 MeV ( Threshold detectors only ) GUESS SPECTRUM LIBRARY: No. REMARKS: The POLYNOM- and PERTURB-results are given in the form of few-group step' fluxes only, so the resuilts of the compari-son of these spectra with the reference 4 given no information about the goodness of the results. The de-tector activities, calculated by us are also wrong.

76

0 2 4 6 8 10 12 1 4 1 6 18 10 11 1011

> w I: ......_

1010 1010 LJ w (f) ......_

N

* * 1 0 9 10

9 I: LJ ......_

z

z 1 OB 1 OB IN2NICU62

X AL271NHEINA24

:::i _J

LL 107

107

_J 5321NPIP32 ([ P 31 1 NP 151 31

NJ581NPICD58 f-z FE541NPIMN54

1 0 6 10 6 w TH2321NFIF ,p,

n::: U2381NFJF.P. w LL !NI 15! NN 1!NI15M LL NP2371NFIF.P.

D 1 05

1 0 5

0 2 4 6 8 10 12 1 4 16 1 8

ENERGY 1 N MEV

ENERGY GRDUP FLUX/REF. FLUX ENERGY INTEGRAL FLUX

0. 5 - 1 .o 1 . 039 Q.5 2.784E+IO 1 . 0 - 1 ,5 1 . 321 1 . 0 l.970E+IO 1 . 5 - 2.0 1. 290 1 . 5 1 .389E+IO 2. 0 - 3.0 1 . 099 2.0 9.781E+09 3. 0 - 4,5 o.907 3.0 4.846E+09 4 . 5 - 6.0 0.921 4 . 5 1 .690E+09 6. 0 - 8.0 0.974 6.0 5.895E+Ö8 5.0-10.0 1 . 125 ß.O 1 .446E+08

10.0- 14.0 0.806 10.0 3.546E+07 14.0-18.0 1 . 487 14. 0 2.034E+06

CHARACTER l ST 1 C INTEGRALS AVERAGEO ACTIVITY OEV!AT!DNS

l 1 l 2 1 3 l4 1 5 1 6 Al A2 A3 R4

ORIGINAL 0.022 o.036 0.023 0 .047 % 8.31% 8. J 6% B. 16%

FEW-GR. 0.017 0.029 0.017 0.039

MR. JONEJR. JNOJR. OJFFERENTIRL FLUX. PRRT OJSC.

F'IG. 37

77

0 2 4 6 8 10 12 14 16 18 1 Ü II 1 o11

> w :L

" 1010 u 1 0 10 w (J)

" N

* * 1 09 1 0

9

:L u

" z

z 1 08 1 0 8

AL271NHEINA24 X :::J _J

LL 107 10

7

_J

CI P3l!NPISl31 NI581NPlC058

f-z FE541NPlMN54 w 1 0

6 TH2321NFIF.P.

~ 1 0 6

0::: U238!NFIF.P. w IN! 15!NNllN115M LL '~" LL NP2371NFIF.P.

' '

0 105 ' 1 0 5

0 2 4 6 8 10 12 1 4 16 18

ENERGY IN MEV


0. 5 - 1 .o 1 .021 o.5 2.760E+10 1 . 0 - 1 . 5 1 . 305 1 .o 1.960E+10 1 . 5 - 2.0 1 .277 1 . 5 1 .386E+10 2. 0 - 3.0 1 . 093 2.0 9.794E+09 3. 0 - 4 . 5 0.910 3.0 4 .883E+09 4 . 5 - 6.0 o.931 4.5 1.717E+IJ9 6. 0 - e.o 0.994 6.0 6.036E+08 8. 0 - 10.0 1 °162 8.0 1 .499E+08

10. 0 - 14. 0 0.842 10.0 3.710E+07 14.0- 18.0 1 .582 14.0 2.163E+06

CHARACTER IST 1 C INTEGRALS RVERAGED ACTIVITY DEVIRTION3

l 1 1 2 l 3 1, 1 5 l 5 RI A2 A3 R,

ORIGINRL 0.023 o.033 0.022 0.043 % 8. 49% 8. 4 4 % 8.44%

FEW-GR. 0.017 0.025 0.016 0.035

n T c-rn•1n" '_) .L V\_.U V 1\ !

FIG. }8

78

0 2 4 6 8 10 12 14 16 18 1011 1 o11

> w L: '--u 1010 w (f)

'--N

* * 1 0 9 10 9

L: u '--z

z 10 8 1 0 8

AL27!NHElNA24

X Tl46CNPlSC46

=i FE56!NPlMN56 _J CU63!N2NlCU62 LL 10 7 D AL27( NP lMG27 10 7

_J c::::::J 532 (NP l P32 C[ c::=:::::::J FE54 C NP l MN54

f-c==:::J NI58( NP lC058

z c::==:J P3l!NPlSI31 w 1 0 6 TH232( NF lF ,p. 10 6

et:: U238!NFJF.P. w LL IN115!NNl!Nll5M LL NP237!NFJf ,p,

D 10 6 1 0 6

0 2 4 6 8 10 12 14 1 6 18

ENERGY IN MEV


0. 5 - 1 .o 1 .039 Q.5 2.616E+IO 1 .o - 1 .s 1 .073 1 .o 1 .802E+IO 1 . 5 - 2.0 o.725 1 ,5 1. 330E+ 10 2. 0 - 3.0 0.813 2.0 1.099E+10 3 .o - 4,5 2 .120 3.0 7.342E+09 4. 5 - 6.0 o.350 4,5 6. 0 - 8.0 1 . 223 5.0 8.0-10.0 5,754 8.0

10.0-14.0 10 .o 14.0-18.0 14. 0


11 1 z 1 3 1 4 1 6 I 5 A1 Az A3 A4

ORIGINAL 7.827 o.090 8.266 o.441 5132.e1 4993.))2 4993.))2

FEW-GR. 5.042 0.053 5. 106 0.296

rrn. JGrffJR. jlfüiR. RB5üi_1.jT STEP tLUXt~ PULYNUf'I

FIG. 39

79

0 2 4 6 8 1 0 1 2 14 1 6 18 1011 1011

> w z '--. u 1010 w (J)

'--. N

* * 10 9 1 0 9 z u '--. z

z 1 0 8 10 8

AL27!NHElNA24

X FE56!NPlMN56

:::J CU63!N2NlCU62 _J D AL27!NPlMG27 LL 10

7 a TI46!NPlSC46 10 7

_J FE54!NPlMN54 er: S32!NPlP32

Nl58!NPlC058 1-· z P31!NPISI31

10 6 106 w TH232!NFIF.P. 0::: U238!NFIF.P. w !Nl 15( NN 1 IN! J5M LL LL NP237!NFIF.P.

0 105 10 5

0 2 4 6 8 10 1 2 1 4 16 1 8

ENERGY IN MEV


0. 5 - 1 .o 2.629 o.5 3.866E+10 1 . 0 - 1 ,5 1 . 239 1 .o 1 .807E+10 1 . 5 - 2.0 0.494 1 ,5 1 .262E+10 2. 0 - 3.0 1 .128 2.0 1 .!05E+10 3. 0 - 4,5 1 . 359 3.0 5.980E+09 4. 5 - s.o o.398 4,5 1 .249E+09 6. 0 - 8.0 1 . 388 s.o 7.73!E+08 8.0-10.0 5,535 8.0 1 • 389E +08

10.0- 14.0 1. 782 10.0 !4.0-18.0 14. 0

CHARACTERISTIC INTEGRALS AVERAGED ACTIVJTY DEVIATIONS

l 1 lz 1 3 14 l 5 l s A1 Az A3 A4

ORIGINAL 10.302 2.306 -93.8102.529 2382.35 2353.23 2353.23

FEW-GR. 6.718 1 . 587 10.310 1.487

MR. JONCJR, INCIR. R650LUT STEP FLuXES

FIG. 40

80

0 2 4 6 8 10 12 1 4 16 18 1 o11 1Ü11

> w L

" 1010 u 1010 w (/)

" N

* * 109

109

L LJ

" z

z 1 06

1 0° CU631N2NICU62

X AL271NHEINA24

=i _J

LL 10

7 1 0

7

_J 5321NPIP32 er: P311NPIS131

~ Nl581NPIC058

f-z FE541NPIMN54

106

1 0 6 w TH2321 NF IF ,P.

Q:'. U2381NFIF.P. ', w LL JN1151NNl!Nll5M LL NP2371NFIF.P.

D 1 0

5 10

5

0 2 4 6 8 10 12 1 4 16 18

ENERGY 1 N MEV


0. 5 - 1 .o 1 . 206 o.5 2.740E+l0 1 .o 1 . 5 0.950 1 . 0 ! .795E+l0 1 . 5 - 2.0 0.947 1 . 5 !.378E+l0 2. 0 - 3.0 1 .082 2.0 !.076E+l0 3. 0 - 4,5 1 '154 3.0 5.902E+09 4 . 5 - 6.0 1 '073 4 . 5 1 .886E+09 6. 0 - e.o 0.953 5.0 6.037E+08 8. 0 - 10.0 1 . 202 8.0 1 .683E+08

10.0- 14.0 1 . 157 10.0 5.164E+07 14.0- 18.0 2.668 1 4 . 0 3.647E+06

CHARACTER 1ST1 C INTEGRALS AVERAGEO ACTJVJTY DEV!ATIONS

11 1 2 1 3 1 ' 15 1 6 A1 A2 A3 A,

ORIGINAL 0.022 0.045 0.020 0.031 % 18.75% 17.61% 17. 61 %

FEH-GR. 0.017 0.027 o.014 0.022

MR. JONEJR. INDJR. RDMM.

?IG. 41

81

0 2 4 6 8 1 0 12 1 4 16 1 8 1 0 9 10 9

> w :L:

' u w 10 8 1 0 8 (/)

' N )1( )1(

:L: u

1 0 7 10? ' z

z

X 1 0 6 10 6

:::J _J

LL CU63!NHElC060 _J FE56!NPlMN56 a: r-

10 5 10 5 z w Cl::: U238!NFJF.P. w LL JN115!NNllN115M LL NP237!NFJF.P.

D 10 4 1 0 4

0 2 4 6 8 1 0 12 1 4 16 1 8

ENERGY IN MEV

ENERGY GROUP FLUX/REF. FLUX ENERGY JNTEGRRL FLUX

0 ,5 - 1 .o 0.695 o.5 2.439E+08 1 . 0 - 1. 5 0.965 1 .o 1 .565E+08 1 . 5 - 2.0 1 .193 1 ,5 9.991E+07 2 .o - 3.0 1 . 213 2.0 6.370E+07 3 .o - 4,5 1 . 065 3.0 2.587E+07 4. 5 - 6.0 o.909 4 . 5 6.682E+06 6 .o - 8.0 0.961 6.0 1 .731E+06 8.0-10.0 o.598 8.o 2.868E+Ö5

10.0-14.0 0.258 10. 0 4.773E+04 14.0-18.0 0 .108 14. 0 1 .307E+03

CHRRRCTERlSTlC INTEGRRLS RVERRGEO RCTIVITY DEVlRTlONS

11 12 1 3 l 4 15 16 R1 R2 R3 R4

ORJGJNRL o.060 0.095 o.033 0.073 23.69% 14. 21 % 14. 21 %

FEW-GR. 0.048 0.074 0.027 0.065

MR. JONEJR. INDIR. DIFFERENTIAL FLUXES ~tRT ~~ISC.

FIG. 42

> w :c

' u w (j)

' N )1(

)1(

:c u

' z

z

X ::::i _J LJ_

_J

a: fz w Cl::'. w LJ_ LJ_

D

82

0 2 6 8 1 8 10 9-t-~+---jf---+~-+-~~-+~-+-~-l----4~-l-~+-~i---+-~-l-~l---J..~~~.t---10 9

1 6 4 10 1 2 1 4

~----'"'""""----------' CU631 NHE JC060 ~---------"~-------' FE561NPlMN56

PlSC46

~--------------' FE54 (NP lMN54 .____ _____ __, U2381 NF lF ,p.

~-----------' JN1151NNl!Nl15M 1-------------' NP2371 NF lF ,p.

10 4-+~-l-~-+-~+-~1----1~-1-~-1-~-1-~-1-~t----l--' ....... ~-l-_.::.-1-~-1-~+----.l----l-

o 2 4 6 8 1 0 1 2 14 1 6 1 8

ENERGY IN MEV


0 ,5 - 1 .o 0.706 o.s 2°477E+08 1 • 0 - 1 ,5 0.980 1 .o 1 .590E+08 1 ,5 - 2.0 1 .213 1 . 5 1 .015E+08 2 .o - 3.0 1 • 232 2.0 6. 472E +07 3 .o - 4,5 1 .081 3.0 2°627E+07 4. 5 - 6.0 0.924 4,5 6°792E+06 6. 0 - 8.0 0.978 6.0 1 . 762E +06

8.0-10.0 0.610 8.0 2.926E+05

10.0-14.0 0.264 10.0 4.889E+04

14.0-18.0 0 .112 14. 0 l . 355E +03

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVITY DEVIATJONS

11 12 1 3 14 15 16

10 8

10 4

ORIGINAL 0.059 0.091 0.034 0.071 24. 16% 14. 98% 14.98%

FEW-GR. o.047 0.069 0.029 0.062

MR. JONEJR, INOJR. DIFFERENTIRL FLUXES OISCOVRY

FIG. 43

83

0 2 4 6 8 1 0 12 1 4 1 6 18 10 9 1 0 9

> w :L '-. u w 1 ÜB ) ÜB (/)

'-. N

* * :L u

10 7 '-. 1 0 7

z

z

X 1 0 6 106 :J

_J

LL TI461NPlSC46 _J FE561NPlMN56 0:: CU631NHElC060

1-C:=J S321NP lP32

z 1 0 5 c:::::J FE54( NP lMN54 1 0 5

w c:==::J NI581NPlC058 et:: C:=J U2381 NF lF ,p. w LL IN1151NNl!Nll5M LL NP2371NFJF.P.

0 104 1 0

4

0 2 4 6 8 10 12 14 1 6 18

ENERGY IN MEV


0. 5 - 1 .o 1 .266 o.5 3.226E+08 1 .o - 1 ,5 1 .169 1 .o 1 .634E+08 1 . 5 - 2.0 0.797 1 ,5 9.486E+07 2. 0 - 3,0 1 . 044 2.0 7.067E+07 3. 0 - 4,5 2.705 3.0 3.809E+07 4. 5 - 6.0 0.288 4 ,5 6. 0 - 8.0 1 . 392 6.0 8.0-10.0 5.237 8.0

10.0-14.0 10 .o 14.0-18.0 14. 0


I 1 1 2 I 3 I 4 I s 16 A1 R2 R3 R4

JRIGINAL 7.077 0 .117 3,740 0. 171 2337.;f6 463.613 463.613

FEW-GR. 4,357 o.076 1 . 719 o.094

MR .. lnNFJP. !~D!~. ABSOLUT STEP rLUXES. rOLYNOM

FIG. 44

84

0 2 4 6 8 1 0 1 2 14 1 6 18 10 9 109

> w :L ......_

LJ w 10 8 108 (f) ......_

N )IE

)IE

:L LJ

10 7 ......_ 10 7

z

z

X 106 1 06 ::::)

_J

LL TI46!NPlSC46 _J S32!NPlP32 er: FE56!NPlMN56

f-10 5

FE54!NPlMN54 z CU63!NHElC060 1 0 5

w 158!NPlC058 O::'. U2 ( NF lF ,p. w LL !Nl 15! NN l INl 1 LL NP237!NFlF.

0 1 0 4 104

0 2 4 6 8 1 0 12 14 16 1 8

ENERGY 1 N MEV

ENERGY GROUP FLUX/REF. FLUX ENERGY lNTEGRAL FLUX

0. 5 - 1 .o 1 . 589 o.5 4.039E+08 1 . 0 - 1 ,5 o.976 1 . 0 2.041E+08 1 . 5 - 2.0 1 . 295 1 . 5 1 . 468E +OB 2 .o - 3.0 1 . 831 2.0 1 .075E+OB 3 .o - 4,5 3.0 5.044E+07 4. 5 - 5.0 o.ao7 4,5 7.868E+07 6 .o - a.o 3,902 5.0 7 .428E+07 s.0-10.0 14°673 8.0 6.842E+07

10.0- 14.0 150.860 10.0 6.256E+07 14.0- 18.0 2935.369 14. 0 3 .543E+07

CHARACTER 1 ST I C INTEGRALS AVERAGEO ACTIVITY OEVIATIONS

I 1 I 2 I 3 I 4 1 5 I 6 A1 Az A3 A4

ORIGINAL 62.759 o.543 72 .918 Q.712 8557.05 1992. )14 1992.)14

FEW-GR. 42.275 0.319 23.672 Q.333

MR • J 0 NE J 8 , l N 0 l r:1 • r:1BS0 LU i ST E P f. L lJ XE S • r' t K r U I< tJ

FIG · 45

85

0 2 4 6 8 1 0 1 2 14 16 18 10 9 109

> w :L

' u w 1 0 8 108 (/)

' N

* * :L u

10 7

' 10 7

z

z

X 1 Os 1 Os ::J _J

lL CU63!NHEJC060 _J FE56!NPIMN56 a: 1-

1 0 5 1 0 5 z FE54!NPJMN5 w Nl58!NPIC058 Cl:: U238!NFJF.P. w lL IN115!NNJIN115M lL NP237!NFJf,p,

D 1 0 4 10 4

0 2 4 6 8 10 12 14 16 1 8

ENERGY IN MEV

ENERGY GROUP FLUX/REF, FLUX ENERGY INTEGRAL FLUX

0 '5 - 1 .o 1 .006 o.5 2.935E+08 1 .o - 1 ,5 1 .178 1 .o 1 .670E+08 1 ,5 - 2.0 1'262 1 ,5 9.786E+07 2 .o - 3,0 1 .136 2.0 5.957E+07 3 '0 - 4,5 0.933 3.0 2.412E+07 4 '5 - 6.0 o.921 4,5 7.319E+06 6 .o - 8.o 1 .217 6.0 2. 307E+06 8.0-10.0 o.935 8.o 4 .778E+05

10.0-14.0 o.548 10.0 1 .044E+05 14.0-18.0 0 '484 14 '0 5.838E+03


l 1 l 2 l 3 l 4 l 5 l s A1 Az A3 A4

ORIGINAL o.027 o.018 0.028 0.025 17.89% 16 .07% 16 .07%

FEW-GR. 0.020 o.009 0.022 0.012

MR. JONEJR. INOJR. RDMM.

FIG. 46

F„B.K. KAM

ORNL UNION CARBIDE CORPORATION NUCLEAR DIVISION

OAK RIDGE, USA

METHOD:

86

The neutron spectrum of a reactor is to be determined from measured

saturation activieies li':t, which are r.elated to the unknown spectrum ~(E)

by the formula

'rhe ai(E) are the cross sections at energy E and the Ci measuring errors

with estirr~ted variance si• ""->

An approximate value ~(Ek) f or the spectrum is obtained by a linear

substitution n

(2) °1(Ek) •L cki e,'i iml

~hose coefficients cki are determined by a method described in the paper:

F. w. Stallmann, Numerical Solution of Integral Equations, Numer. Math. ~

297 00305 (1970).

Applied to this particular problem the numerical procedure may be

interpreted as follows: let'\f(E) be a rough guess for the spectrum and the

integral

be a measure of the deviation of the computed spectrum from the guessed

spectrum. The program attempts to minimize S~ subject to the condition that

the dif f erence (i bet:ween computed and measured activities

87

falls within a given range; more specifically the accumulated variance

should be less than a given constant. (The expected value of f is n, the ,..J

number of foils, if ~(E) is the true spectrum.) ,.J

This procedure may lead to negative values of ~(E) if the guessed

spectrum 'f(E) deviates too much from the true one and the limit of f in

(5) is too small. To avoid this a stepwise approximation is used. The

procedure starts with an initial guesslf (E) and a limit for f which is

large enough to yidd nonnegative values of ~(E). (This is dways possible,)

The values of ~(E) are then used as a new guessed spectrum and the procedure

is repeated with increasingly lower values of f in (5). The procedure is

terminated once this limit is within an acceptable range. If no solution

exists within this range the procedure converges to a solution with the

smallest value of f.

SPECTRA PROCESSED: I. Spectrum ( 3 results ) II. Spectrum ( 3 results )

I 0 A0 - I.B. - I„~ - Thr~ee different spectra have been obtai

ned using different guess spectra ( Fig 47 - 52. ) II 0 D0 - II„E. - II 0 F. - as by the I. Spectrum ( Fig. 53 - 58.)

REPRESENTATION MODE OF THE RESULTS: 621-point differential

spectra„

ENERGY REGION: 10-iO - 18 MeV

GUESS SPECTRUM LIBRARY: Yes

REMARKS: No

> w L ....... u w (/")

....... N )!(

)!(

L u ....... z

z

• ....J CI

fz w a::: w lL lL

0

88

0 2 4 6 8 10 12 14 1 6 18

1010 CU63fN2NlCU62

~----------' 1127 ( N2N l I 126 ~-----------' MG24f NP lNA24

.__ _________ ...J U238 f NF l F.

'------------' INl 15( NN l IN115M '--------------' NP237f NF lF ,p.

) 0 7-H=::::======::::J PU239f NF lF ,p. '----------' U235( NF lF ,p . ~---~ FE5BfNGlFE59 I'------' U238( NG lU239

1~-----~ NA23fNGlNR24 1 0 6'-i:::::::::==:::J C059( NGlC060

o----~ SC45( NG lSC46 P----~ AU197fNGlAU198 o------~ CU63f NG lCU64

10 5--+-~-l-~-+-~+-~+----+~-+~-l-~-+-~-+-~.j.----<l---;.~-1-~-i-~-1-~.j.---'>....,.--l-

o 2 4 6 8 1 0 1 2 1 4 1 6 1 8

ENERGY 1 N MEV


0. 5 - 1 .o Q.949 o.5 2.435E+10

1 • 0 - 1 ,5 1 .008 1 .o 1 .691E+10

1 • 5 - 2.0 1 .043 1 ,5 1.248E+1 O

2. 0 - 3,0 Q.958 2.0 9 .160E+09

3. 0 - 4. 5 Q.889 3.0 4.856E+09

4. 5 - s.o Q.981 4 ,5 1 .759E+09

6 .o - 8.Q Q.971 6.0 5.867E+08

8.0-10.0 1 • 076 8.Q 1 .433E+08

10.0 - 14.0 Q.897 10.0 3.888E+07

14.0-18.0 1 . 215 14. 0 1 .661E+06

CHARACTERISTIC INTEGRALS AVERRGEO ACTlVITY OEVIATIONS

l 1 l 2 I 3 l 4 1 s l s A1 A2 A3 R4

ORIGINAL Q.006 Q.004 Q.294 Q.006 Q.004 Q.035

1 0 10

1 0 6

1 0 5

5. 43% 5.89% 5. 43% 5.89% FEW-GR. Q.004 0.002 Q.276 Q.004 0.002 Q.055

MR. KRM. USR. SPECTRUM * * R * *

FIG. 47

1 o-10 1 o-9 10-8 10-7 10-6 10-5 10-4 10-3 1 0-2 1 0-1 10° 101

1 02

10111 1 1 1 1 1 1 1 1 1 1 1 1

1011 -> w L

' u 10 1~ / \. +iolO w

())

' N

* * CU63 l N2N l CU6~ 0 L 1127lN2Nlll26 0 u 109 MG24lNPJNA24 CJ +iog ' z AL27lNHEJNA24 ~ FE56lNPJMN56

"'.J H z AL27lNPJMG27 0

~ Tl46lNPJSC46 . X 10

8 S32lNPJP32

~ tlOa _.,..

FE54lNPJMN54 CO :::l _J P31 l NP JSl31 Q'.)

lL Nl5B!NPJC05B \.0

_J TH232lNFJF.P. a: U23BlNFJF.P. ~

107 IN115lNNJINll5M c::::::=J 1 +io

1 r- NP237lNFJF.P. z w PU239lNFJF.P. O::'. U235lNFJF.P. w LL FE5BlNGJFE59 LL U23B!NGJU239 ~

106 1 +io

6 NA23lNGJNA24 0 C059lNGJC060

SC45lNGJSC46 AU197!NGJAUJ9B

CU63!NGJCU64

105

1 !

1 1 1 1 \ 1 1 1 1 1 1 1 1 1 0

5

1 0 -10 1 0-9 1 o-a 10-7 10-6 1 0-5 1 o-4 10-3 1 0-2 10-1 10° 101

1 02

FNERGY IN MEV

MR. KAM. USA. SPECTRUM • • A • •

> w l::

' u w (f)

' N )1(

)1(

l:: u

' z

z

X ::J _J

LL.

_J C[

z ..LJ '.l::'. ..LJ LL. LL.

0 2 4 6

10 7'-J-E:=======::::i PU239( NF lf ,p, '-----------' U235( NF lf ,p. •----~ FE58(NGlFE59 ..__ ___ __, U238 ( NG l U239 ~---::::::::J NA2 3 ( NG l NA2 4

1 0 6'-if::::::::=~ AU 1 97 ( NG l AU 1 98 1~--~ SC45! NG lSC46 I'----' C059! NGlC060 o------~ CU63!NGlCU64

90

8 10 12 1 4 16 18

CU63!N2NlCU62 1010

10 5'-t---l-~+----<l---l---l--~..J.--+----+--l---l--+---+--l---l--+----<i--,;:,;,i..---1-- 1 05

0 2 4 6 8 1 0 1 2 1 4 16 18

ENERGY IN MEV


0 '5 - 1 .o Q.815 o.5 2°312E+l0 1 . 0 - 1 . 5 Q.945 1 .o 1 .674E+IO 1 . 5 - 2.0 1 .059 1 ,5 1 .259E+IO 2. 0 - 3.0 Q.996 2.0 9.214E+09 3. 0 - 4,5 o.830 3,0 4.740E+09 4 '5 - 6.0 1 .048 4. 5 1 .851E+09 6. 0 - 8.0 1 .006 6.Q 5 .993E+08 8.0-10.0 0.993 8.o 1 .397E+08

10.0-14.0 1 .Ql 4 10 .o 4 .332E+07 14.0-18.Q o.899 14. 0 1 . 229E +06

CHARACTERJSTJC INTEGRALS AVERAGEO ACTIVITY OEVIATIONS

11 1 2 1 3 14 1 5 16 A1 A2 A3 A4

4.02% 4. 02% 4.02% 4. '12% ORIGINAL 0.012 Q.027 Q.288 Q.014 Q.026 Q.087

FEN-GR. 0.007 0.022 0.227 0.010 Q.025 Q.052

MR. KRM. USR. SPECTRUM • • B * •

FIG. 49

i o-10 1 0-9 1 o-e 1 o-7 1 o-6 10-s 1 o-4 1 o-3 1 0-2 1 0-1 10° 1 0 l 10 2

1011 1011 -> w ::c '-u

1014 // ~ +iolO w

(f")

'-N

* * ::c u

109 MG24! NP lNR24 - . \o +ios '-z RL27 ! NHE l NR: - FE56!NPlMN56

"'.) H z RL27!NPlMG27 Q - TI46!NPlSC46 .

108 S32!NPlP32

~ rlOe VI X FE54!NPlMN54 0 =:J

_J P3!!NPlSl31 \.0 LL N!58!NPlC058 ....... _J TH232! NF lF .P. a: U238!NFJF.P. - 10

7 INllS!NNl!Nl!SM c:::::::::J 1 +io7

f- NP237!NFJF.P. z w PU239!NFJF.P. a::: U235!NFJF.P. w LL FE58!NGlFE59 LL U238!NGlU239 - 10 6 1 +io

6 NR23!NGlNR24 0 RU!97CNGlRU!98

SC45CNGlSC46 C059CNGlC060

CU63CNGlCU64

10

5

'

! 1 1 1 11

1 1 1 1 1 1 1 I 1 10

5

1 o-10 1 0 -9 10·8 1 o ·7 10-6 1 o-s 1 o-4 10-3 1 0-2 1 0-1 1 0° 101 1 02

ENERGY IN MEV

MR. KAM. USA. SPECTRUM • • B • •

> w L: ....... u w (/) ,, N

)1(

)1(

L: u ....... z

z

X :::> _J

LL

_J

CI

1-z w Q:'. w LL LL

0

92

0 2 4 6 8 1 0 1 2 1 4 16

CU63lN2NJCU62 1010 '------------' 1127l N2N J 1126

.-----------~ MG24l NP JNA24

'----------------' AL27( NHE JNA24

C~~~~================iRl~~p'JFE56(NPJMN56 AL27(NPJMG27 TI46(NPJSC46

S32lNPJP32 FE54lNPJMN54

1 (NP JSI 31 58(NPIC058

::::==========-:-::' TH23 1 F • P. '-----------....J U238 ( NF J F.

'-------------' INl 15( NNJ INl 15M .__ _______ ___J NP237( NF JF ,p.

1 0 7'-fi=::::======:::::i PU2 39 ( NF J F • P • 1'--------....J U235l NF JF ,p. •'----~ FE58(NGJFE59 I'------' U238 ( NG l U239 l'-------....J NA23( NG JNA24

1 0 6·-t::::::::====:::i CU63( NGJCU64 11----....J C059( NG IC060 r------' SC45l NG JSC46 ,__ __ __J AU! 97( NG JAUi 98

18

10 5---+-~-l-~.j-....---l~--4-~-4-~-+-~l---..j.~-l-~-+-~.j-....--l~-l-~-l--~-l---l>---.::.i>~-*-

o 2 4 6 8 10 1 2 14 16 18

ENERGY IN MEV


0. 5 - 1 .o 0.934 o.5 2.428E+10

1 • 0 - 1. 5 1 .020 1 .o 1 .696E+IO

1 • 5 - 2.0 1 .031 1 • 5 1 • 247E+10

2 .o - 3.0 o.964 2.0 9.192E+09

3 .o - 4.5 o.892 3,0 4.861E+09

4. 5 - 6.0 o.980 4,5 1.754E+09

6. 0 - s.o 0.959 6.0 5.828E+08

8.0-10.0 1 .076 8.0 1 .449E+08

10.0-14.0 o.939 10 .o 4 .043E+07

14.0-18.0 1 • 083 14. 0 1 .481E+06


11 1 2 1 3 1 4 l 5 l s A1 Az A3 A4

ORIGINAL 0.006 o.006 0.584 0.006 0.006 o.081

1010

106

5.24% 5.34% 5.24% 5.34% FEW-GR. 0.004 0.003 0.535 o.004 o.004 0.037

MR. KRM. USR. SPECTRUM * * C * *

FIG. 51

1 o-10 10-9 i o-s 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10° 101 102 1 Ü II 1011

~

> w :L ........ u

10 1~ [/ \ +iolO w ({) ........ N llE llE :L u

l09t ~ I \o +ios ........ MG24(NPJNA24

z AL27(NHEJNA24 FE56(NPJMN56

>otj z AL27(NPJMG27 H - TJ46(NPJSC46 0 S32!NPJP32 . X 106 ci +io0 \.0

:::J FE54(NPJMN54 v;i V1 _J P3!(NPJSl31 r\)

LL NJ5ß(NPJC058 _J TH232(NFJF.P. a: U238(NFJF.P. - 107 IN1!5(NNJIN115M ~ 1 +ro7 r--z NP237(NFJF.P. w U239!NFJF.P. a::: w LL LL - 1 0 6 NA23!NGJNA24 1 +io6 0 CU63(NGJCU64

C059(NGJC060 SC45(NGJSC46 AU197(NGJAU198

105

1 !

1 1 1 1 1 J

1 1 1 1 1 1 I 1 105

1 o-10 1 o-s 10-e 10-7 10-6 10-5 10-4 1 o-3 10-2 10-1 10° 101 102

ENERGY IN MEV

MR. KAM. USA. SPECTRUM • • C • •

94

0 2 4 6 8 10 12 14 16 1 8 1 0

9 1 09

\ > 1 w :L '-LJ w 1 0

8 1 0 8 (f) 1127 ( N2N 11 1 26 '- MG241NPINA24 N

)!(

* CU63 ( NHE l C060 :L FE56(NPIMN56 LJ '- 10

7 Tl46(NPISC46 107

z S32(NPIP32 FE54(NPlMN54

z NISBINPIC058

X 10

6 => 1 0

6

_j

LL

_j

a: FE58(NGIFE59

f-10 5 1 0

5 z

~ w U235(NFIF.P. et:'. PU2391NFIF.P. ~ w SC45(NGISC46 LL LL

D 1 o• "' 104

0 2 4 6 8 10 12 1 4 16 1 8

ENERGY 1 N MEV


0. 5 - 1 .o Q.945 Q.5 2.737E+OB 1 . 0 - 1 ,5 1 . 138 1 .o 1 . 550E +OB 1 . 5 - 2.0 1 . 1 78 1 . 5 8.821E+07 2. 0 - 3.0 Q.958 2.0 5.248E+07 3. 0 - 4. 5 0.696 3.0 2°25BE+07 4. 5 - 5.0 1 . 374 4 . 5 1 .004E+07 6. 0 - 8.0 1 . 420 5.0 2.55BE+06 8.0-10.0 o.772 s.o 4.24BE+05

10.0-14.0 0.326 10.0 1 .163E+Ll5 14.0-18.0 4 .783 14. 0 5. 772E +04

CHRRRCTERISTJC INTEGRRLS RVERRGEO RCTIVITY OEVIRTIONS

l 1 1 2 1 3 14 15 l s RI . R2 R3 R4

ORJGINRL 0.247 0.039 2.34E+2 0 .225 0.037 2.63E+2 7.86% 10. 4 1 % 7.86% 10.41%

FEW-GR. 0.088 0.007 50.768 0.089 0.008 32.088

1·1R. !\Hf1, UoH. ::31-'t.iRUM" "u""'

FIG. 5~

!.!'.

°'

> w L: ....... LJ w (f)

....... N llE llE L: LJ ....... z

z

X :::l _J

LL

_J

a: fz w a::: w LL LL

D

1 o-8 10-6 1 o-3 1 0

1

10-10

10-9

10 12 1012 1 0

2 1 0-2 1 0 -s 1 0 -4 10- 1 10° 1 o-7

1011

1010

109

108

107

106

NR231NGlNR24 CU631NGICU64

FE581NGIFE59

I 1271N2N1I126

RL~l.NHE lNR24 CU (NHE lC060

FE56 Nf>]MN56 St46

FE541NPlMN54 NI581NPIC058

TH2321NFIF.P. U2381NFJF.P.

IN! 151 NN l IN! !SM NP2371NFIF.P.

~~~~~~~~~~ MN551NGIMN56 C0591NGlC060 U2351NFIF.P.

PU2391NFIF.P. SC451NGISC46

RU!971NGlRU!98 r-~~~~~~~~~~~~~~~~

D CJ c::::J CJ c=i

10 II

1010

109

1 08

107

1 06

1 Os 1 Os 10- 10 10-9 1 0-0 1 0-7 1 0 -6 1 o-s 1 0 -4 1 0 -3 1 0-2 1 0- 1 10° 101 1 0 2

ENERGY IN MEV

MR. KAM. USA. SPECTRUM * * D * *

"<!'" U"\

ü H li.

> w L: 'u w (/)

'N

* * L: u 'z

z

X ::::> _J

LL

_J

0:

1-z w O'.'. w LL LL

0

96

0 2 8 18 10 9·-t-~+-~+-~1---+~-+--~+-~+----1-~-J-~-l-~+----i.~-l-~-l-~+----i.~-J..~-1---10 9

16 4 6 10 12 1 4

I 1271N2N1I126 .__ _____________ __,MG241NPINA24

~-----------------' AL271NHE1 NA24 ~-------------___J CU631NHEIC060

.__ _______________ ___J FE56!NPIMN56

..___._-~--------' TI461NPISC46 c=3:;;;;:2S;;:~===::::i S 3 2 1 NP l P 3 2

'---------".4----_,FE541NPJMN54 ~------____,,. __ ___, N l 5b 1 NP l C 058

1 F lF. P. N

~------~ NP2371 NF lF ,p.

FE581NGIFE59

1------' U2351NFJF.P. 1----~ PU2391NFJF.P.

C0591NGIC060 AUl971NGIAUl98

10 4-l-~-+-~4-~+-~1----1-~-1-~-i-~-+-~+--'-4-"----l~-+~-l---"-+-~+-.::.,_+-~i----l--

o 2 4 6 8 10 12 1 4 16 18

ENERGY 1 N MEV


0. 5 - 1 . 0 1 .065 0.5 2.818E+08 1 . 0 - 1. 5 0.995 1 .o 1 .478E+08 1 . 5 - 2.0 1. 188 1 . 5 8.947E+07 2. 0 - 3.0 0.995 2.0 5.342E+07 3. 0 - 4. 5 0.679 3.0 2.239E+07 4,5 6.0 1 . 403 4 . 5 1.017[+07 6. 0 - 8.0 1 . 405 6.0 2.528E+06 8.0-10.0 0.742 8.0 4.l68E+05

10.0-14.0 0. 460 10.0 1 .205E+05 14.0-18.0 3. 130 1 4 . 0 3.777E+04

CHARACTER l ST IC INTEGRALS AVERAGEO ACTIVITY OEVIATIONS

I 1 I 2 I 3 !4 I s I 6

104

ORIGINAL 0.275 0.028 1 . 01 E +2 0.252 0.030 76.642 7. 77% 10.29% 7.77% 10.29%

FEW-GR. 0.093 0.005 32.549 0.092 o.006 16.933

MR. KRM, IJSR. SPFrTRllM " "' F;: " -.

FIG. 55

1:-0'\

> w ::L 'u w (f)

'N

* * ::L u 'z

z

X :::J _J

LL

_J

a: tz w 0:::: w LL LL

0

1 o-a 1 o-7 1 o-6 1 0 -S 101

10-10

10-9

10 12 1012 10

2 1 0- 3 1 0- 2 1 0 -4 1 0° 10- 1

1011

109

1 0 8

107

106

NR231NGJNA24 SC451NGJSC46

CU631NGJCU64 FE581NGJFE59

11271N2Nll126 0 241NP:NA24

R~71 NHE JNR24 cu5~(_NHE 1 C060

FE5 1Nf>,~MN56 T 1461 IS(\46

FE541NPIMN54 Nl581NPIC058

TH2321NFJF.P. U2381NFJF.P.

!Nl 151NN1 IN! !SM NP2371NFJF.P.

'---------__) MN551 NG IMN56 U2351NFJF.P.

PU2391NFJF.P. '------------'C0591NGJC060

RUJ971NGJRU!98

i oll

1010

1 09

1 08

107

106

10 5 105

1 0- 10 1 o-9 1 o-8 1 o-7 1 o-6 10-5 1 o-4 i 0- 3 1 0-2 1 0- 1 10° 101

1 02

ENERGY IN MEV

MR. KRM. USR. SPECTRUM * * E * *

"' "' 0 H ~.

98

0 8 18 lQ 9-r~-t-~+---l~-+~-+-~+-~l---+~-+~-l-~{---+~-i-~-1-~.f-.--+~-1-~-1-10 9

2 4 6 10 16 12 14

> w :L

" u w (f)

" N

* * :L u

" z

z

X ::J _J

IJ_

_J

a:

1-z w Cl::'. w IJ_

IJ_

0

1 0 8

107

1 0 6

1 0 5

10 4

ORIGINAL

FEW-GR.

0

1 127 ( N2N l 1126 RL27!NHElNR24

'---------------------' MG24!NPlNR24 c__ ______________ __J CU63!NHElC060

,..-..·~---------------------' FE56!NPlMN56 '-~-f----,\,----------' T 1 4 6 ( NP l SC 4 6

'---+---.P...-+---__, S 32 ( NP l P 3 2 ..._ __ ...__,__--->.-1------' FE 5 4 ( NP l MN5 4 '----+---+---~--__J N 1 5& ( NP l C 05 B

NR23!NG!NR24 SC45!NGISC46

PU239!NFIF.P. U235!NFJF.P.

RU197!NGlRU19B FE5B!NGlFE59

MN55!NG!MN56 C059!NG!C060

2 4 6 8 10

ENERGY GROUP FLUX/REF. FLUX

0. 5 - 1 .o 1 .083 1 . 0 - 1 ,5 0.950 1 . 5 - 2.0 1 . 126 2. 0 - 3.0 1 . 154 3. 0 - 4. 5 o.442 4 . 5 - 5.0 1 . 740 6. 0 - s.o 1 .168 s.0-10.0 1 . 030

10.0-14.0 o.431 14.0-18.0 4.232

12 1 4 16

ENERGY 1 N

ENERGY INTEGRAL FLUX

o.5 2.818E+08 1 .o 1 .456E+OB 1 . 5 8.991E+07 2.0 5.574E+07 3.0 1 .972E+07 4,5 1.177E+07 6.0 2.296E+06 8.0 5.400E+05

10.0 1 .286E+05 14.0 5.108E+04

10 6

104

18

MEV

CHRRRCTER 1ST1 C I NTEGRRLS RVERRGEO RCTlVITY DEVlRTIONS

11 1 2 l 3 14 15 1 s

0. 511 0. 1 71 0.551 o.541 0. 162 0.092 6.91% ß.99% 6.91% 8.99%

0. 146 0.009 o.324 0. 154 O.OOB 0.025

~~ n 1/ n P • •,.... r. 'II\ o l\r'\ ; J U._,f-; •

FIG. 57

1 o-10 10-9 10-8 1 o-7 10-6 10-s 1 o-· 1 o- 3 1 0- 2 10-1 1 0 ° 101

1 02

1012 1012 ~

> w L: .......

1011+-- /\ +1011 LJ

w r.n ....... N llE llE lül / \

+1010 L: LJ l ....... '< l127!N2Nlll26 ~ z

/ 4!NPJNR24 CJ

z 101 C 6 JNHEJC060 CJ t109

~

/ FE IN't>-~MNS6 c::=:::J

(l() O'I Tl46 NPIS(:46 CJ LI"\ O'I X

S32<Ne 32 (@ :::J _J FES4! NP J 54 \ ===:J

+108 ö

LL 10

8 NIS8!NPIC . r:::::=:::J i-;

T„,...„.„..,, „,,-, r ii< _J

er: ~ !Nl JS! NN 1 lNl lSM t---

NP237!NFJF.P. z 1 w 10

7 NR23ING1 NR24 \ J\ +107

0::: SC4S!NGISC46 w LL P 239!NFJF.P. LL U2 S!NFJF.P. ~ CU 3!NGJCU64 0

1 06 RU197!NGIRU1~~~ +10

6

FE58 NGJFE59 MNSS!NGJMNS6 COS9!NGJC060

1 05

1 1 1 1 1 \ 1 1 1 q 1 105

i o-10 1 0-9 1 o-8 1 o-7 1 o-6 1 0 -s 1 0 -· 1 o-3 1 0-2 1 0-1 10° 101 102

ENERGY l N MEV

MR. KRM. USR. SPECTRUM * * F * *

100

G.C. ::IARTIN

GEHER AL ELECTIUC, PLEASA:JT~';N, USA

M:STHOD: RDMJ'vI /5/

SPECTRA PROCESSED: I. Spe et rum I' 1 result, Fig. 59 and 60 \.

II. Spectrum I'

result, Fig. 61 and 62 \.

REPTIESE:~TATION MOD~ OF TEE RESULTS: 280-point differential

spectrum

.SI:-ERGY :\EGION: 1 o-9 - 1 4 MeV.

GUESS SPECI'Il.UM LIBRARY: No

REMATIKS: No

)

)

> w I: ....... u w (/)

....... N

* * :L u ....... z

z

X => _J

LL

_J

a: rz w Q:'. w LL LL

D

101

2 6 0 10'..,..~;-~r---1~-1-~+-~+----jf---+~-+-~+-~1---+~-l-~+-~l---+~-l-~4-1011

1 4 16 4 1 0 18 12

~~...,__-----~ AL271 NHE lNA24

C~~~~~~~~~~~~~Tl461NPlSC46 PlMN54 Nl58! 058

~~~~~~~~~~~~ TH232! NF lF. C U238!NFlf,p, c__ ________ __, NP237! NF lF ,p.

'-----------' PU239! NF lF ,p. L----------' U235! NF lF ,p. '-----~ FE58! NG lFE59 !'--------' NA23! NG lNA24

10 6-t:::::::=:::J AU197!NGlAUl98 11------' SC45!NGlSC46 1----~ C059! NG lC060 11--------' CU63! NGlCU64

10 5-+~+----j~-t-~-1-~t--+~-+-~+---t~-+~-+-~f---+~+-~l---+~""'I-~~

0 2 4 6 8 1 0 1 2 14 16 18

ENERGY IN MEV


0. 5 - l .o l .091 o.5 2.597E+l0

l .o - l ,5 l .203 l .o l. 743E+ l 0

l • 5 - 2.0 l .072 l ,5 l.2l4E+l0

2. 0 - 3,0 Q.867 2.0 8 .725E+09

3 .o - 4,5 Q.807 3.0 4.83lE+09 4 ,5 - 6.0 l .051 4,5 2.020E+09

6 .o - 8.0 l • 343 6.0 7.642E+08

8.0-10.0 l • 540 8.0 l .5lOE+08

10.0-14.0 Q.045 10 .o l .540E+06

l 4. 0 •· l 8 .o l 4 .o

CHARACTER 1 ST I C INTEGRALS AVERAGEO ACT!VITY OEVJATJONS

11 12 I 3 l 4 1 5 l 5

1010

1 0 5

ORIGINAL 0 .111 0.019 o.308 0°063 0.015 0.063 22.51% 33.14% 4.34% 5-39%

FEW-GR. 0 .097 0.016 0.294 0.051 0.013 0°085

MR. MP.RT!N. USR.

FIG. 59

1 o-10 1 0-9 10-8 10-7 i o-s 1 o-5 1 o-4 1 0-3 1 0-2 i 0-1 10° 101 102 1011 1 Ü II

~

> w L ........ u

1 0 1.!!f- / ~ +iolO w (f)

........ N llE llE L u

109+ // \ 10

9 ........ z -

C\J z 0 -""""" 0

X 108

108 \.0

::::l . _J AL27LNeE,NA2' ~ {.' LL T;46(NPlSC46 c::J H

~ _J FE54(NPlMN54 c::::J a: Nl58(NPlC058 ~ - 10

7 TH232 ( NF l F . P. c:::::J 1\ +io

1 1-z U238(NFJF.P. c:::::J w NP237(NFJF.P. Q:'. PU2391NFJF.P. w LL U235(NFJF.P. LL FE58(NGlFE59 - 10

6 1\ +ios NR23(NGlNR24

D RUJ97(NGlRUJ98 SC45(NGlSC46 C059(NGlC060 CU63(NGlCU64

105

1 /

1 1 1 ~ 1 1 1 1 1 1 111

1 105

i o-10 10-9 10-8 10-7 10-6 i o-s i o-• 10-3 1 0-2 1 0- 1 10° 101

102

ENERGY IN MEV

MR. MARTIN. USA.

103

0 2 4 6 8 10 12 1 4 1 6 1 8 10 9 1

109

> w :L

" u w 1 0 6 10 6 (f)

" N

* * :L u

1 07

" 107

z RL27lNHElNR24

z Tl46!NPlSC46 FE54!NPlMN54

X 1 0 6 1 0 6

:::i _J

LL

_J NR23!NGlNR24 er: SC45!NGlSC46

f-10 5 FE58!NGlFE59 10 5

z w U235!NFlF.P. Q::'. PU239!NF1f,p, w

C059!NGIC060 LL LL AUl97lNGlAUl98

D 104 10 4

0 2 4 6 8 1 0 12 14 16 18

ENERGY 1 N MEV


0. 5 - 1 .o 1 . 118 o.5 2.779E+08 1 . 0 - 1 . 5 o.890 1 . 0 1 .373E+08 1 . 5 - 2.0 o.881 1 . 5 8.512E+07 2 .o - 3.0 1 . 025 2.0 5.838E+07 3 .o - 4,5 1 . 041 3.0 2.640E+07 4. 5 - 5.0 o.991 4 . 5 7.646E+06 6. 0 - 8.o 1 . 167 6.0 2.248E+06 8.0-10.0 o.894 8.0 4.947E+05

10.0- 14.0 o.752 10. 0 1 . 376E +05 14.0-18.Q 0. 041 14 . 0 4.896E+02

CHARACTERISTIC INTEGRALS RVERRGEO ACTIV!TY OEVIRTJONS

l 1 1 2 l 3 !4 l s l s A1 A2 R3 A4

ORIGINAL o.01s 0.018 36.978 0.012 0.018 32.029 15.05% 13.62% 10.96% 3.64%

FEWJ.OI,. 0.011 0.013 9.688 0.008 0.013 7.226

MR. MRRTlN. IJSR

FIG. 61

i o-10 10-9 10-8 10-7 i o-s i o-s i o-· i o- 3 10-2 1 0 -J 1 0° 101

1 02

10121 1 1 1 1 1 1 1 1 1 1 1

1

1012 -> w ::c '--

1011+- /\ +1011 LJ

w (f)

'--N JI(

JI(

10 1~ r ~\ +1010 ::c ' .,

LJ '--z -z l0

9t // \~ ( ~ t109 "'<!'- ~

("\J

0 \!)

..- X :::J 1 0 __j RL27l NHE 1~24 CJ H LL

108 Tl46lNPISC46 c:::::J 10

8 li<

__j FES4lNPIMNS4 a: N!S8lNPICOS8 ~ TH232lNFJf.P. f-z U238lNFIF.P. w 10

7 NP237lNFJF.P. +107

~ NR23lNGJNR24 w LL SC4SlNGJSC46 LL CU63lNGJCU64 ~ FES8lNGIFE59 0

106 \ +10

5 U23SlNFJF.P.

PU239lNFJF.P. C059lNGIC060

RU197lNGJRU!98

i 05 I ' 1 1 1 1 1 1 1 1 1 \ 1

1 0 s 1 o-10 1 0-9 10-8 10-7 1 o-6 i o-s 1 o-• 1 0 -3 1 0-2 1 0-1 10° 1 0 l 1 0

2

ENERGY IN MEV

MR. MRRTIN. USR.

105

W ..N. McEI,ROY

WADCO, USA.

lV!ETHOD: SAND-II. /17/.

SPECTRA PROCESSED: I. Spectrum ( result, Fig. 63 and 64. ) II. Spectrum ( 1 result, Fig. 65 and 66. )

REPRESENTATION MOD~ OF THE RESULTS: 630-group spectra

ENERGY REGION: 10-10 - 18.0 MeV

GUESS SPBCTRUM LIBRARY: '.~es.

REMARKS: These spectra have been used by us as a reference"

> w L:

" u w <J)

" N

* * L: u

" z

z

X :::J _J

LL

_J

er:

fz w Cl::'. w LL LL

0

0

1010

106

2 4 6 8 1 0 12 1 4 1 6

CU63tN2NlCU62

'-----------' 1127tN2Nll126 .-----------~ MG24( NP lNA24

~----------~ AL27( NHE lNA24

~~S::;==~~~~~~~~~~~~FE56tNPlMN56 C: AL27 (NP l MG27

===~~~~~~~~~~~~ T 146 (NP l SC46 C: S32tNPlP32

;==:======~~= FE54tNPlMN54 1 (NP l S 131

~---------~ 8(NPIC058

'------------' TH23 F lF. P • .__ ________ __, U238 ( NF l F.

._ _______ __, !Nl 15(NNl!Nl 15M .__ _______ __, NP237( NF lF ,p.

1 0 7'---f1~============:::::i PU 2 3 9 ( N F l F • P • ._ _______ _, U235( NF lF ,p. .__ ___ __, FE58(NGlFE59

1~---~ U238(NGlU239 I'---------' NA23( NG lNA24

1 0 6'-f'::======= SC45tNG l SC46 ,__ __ __, AU 197 ( NG l AU 198

IL----~ C059 ( NG l C060 r--------' CU63( NG lCU64

18

10 5-1-~--t-~--r-~-1--~~~1---~~--1-~--t-~-1--~-1-~~---;F--~~--1-~--t-~-+-~>+-~+-

o 2 4 6 8 1 0 12 14 16 1 8

ENERGY IN MEV

l 1

E NERGY GROUP

0. 5 - 1 '0 1 . 0 - 1. 5 1 . 5 - 2 '0 2.0 - 3.0 3.0 - 4,5 4,5- 6.0

s.o- 8.0 8.0-10.0

10.0 - 14.0 14.0-18.0

FLUX/REF. FLUX

1 '000 1 • 000 1 • 000 1 .ooo 1 .ooo 1 .ooo 1 .ooo 1 .ooo 1 .ooo 1 .ooo

CHARACTERISTIC INTEGRALS

ENERGY INTEGRAL FLUX

Q.5 2.518E+l0 1 .o 1 • 735E + 10 1. 5 1 .295E+l0 2.0 9.765E+09 3,0 5.273E+09 4,5 1 • 792E +09 s.o 5.967E+08 8.0 1 .399E+08

10.0 4.286E+07 14. 0 1 • 367E +06


Al A2 A3 A4

10 5

ORIGINAL 0.000 0.000 0.000 o.ooo o.ooo o.ooo o.ooo o.ooo o.ooo 4 '11 % 3.89% 4 .11 % 3.89%

FEW-GR. 0.000 0.000 0.000

MP MCEL.ROY. 1• 15R. REFERENCE SPECTRUM

FIG. 6)

1 o-10 1 o-9 1 o-a 10-7 10-6 1 o-s 1 o-4 10-3 1 0-2 10-1 1 0° 101 102

1 0 ll 1011 ~

> w :E

" u 10 14 / \ +io

10 w (f)

" N

* * :E u

109t r \o +io9

" MG24CNPlNA24

:z AL27(NHElNA24 FE56(NPlMN56

:z AL27(NPlMG27

1:-~ Tl46CNPlSC46

! +o· ... \C

0 X 10 8 S32(NPlP32 ..... :::::> FE54CNPlMN54

CCl _J P31CNPJS131 H

LL Nl58(NPJC058 ~

_J TH232 C NF l F . P . er: U238(Nflf.P. ~

10 7 IN115CNNJINll5M c:::::::::::J 1 +io

1 1-:z NP237CNFJf.P. w PU239(Nflf.P. Cl:'.: U235CNFJf.P. w LL FE58(NGJFE59 LL U238CNGJU239 ~

106 NA23CNGJNA24 1 +io

6 0 C059(NGJC060

SC45(NGJSC46 AU197CNGlAU198

CU63(NGJCU64

105

1 !

1 1 1 1 1 1 1 1 1 1 , 1

1 1 05

i o-10 10-9 10-8 10-7 10-6 10-s 10-4 1 o-3 1 0-2 10-1 1 0° 101 102

ENERGY IN MEV

MR. MCELROY. USR. REFERENCE-SPECTRUM

> w :L 'LJ w (f)

'N

* * :L u 'z

z

X :::)

_J

LL

_J

er: fz w et:'. w LL LL

D

108

0 8 1 8 10 9·---r~-r-~t--~~--t-~+.---ii---4-~-l--~.j.---4~-+-~-l--.J~-+-~-l-~l-----J.~-l-10 9

16 2 4 6 1 0 12 1 4

1127 ( N2N l 1126 MG24!NPlNA24

-~~~~~~~~~~~~~ AL27! NHE lNA24 , CU63 ( NHE l C060 ,__ ___________ __J FE56 (NP l MN56

~.,....-------------' T 146 (NP l SC46

~~~~~~~~~~S~32! NP lP32 ;::_ FE54 (NP l MN54 '---------->.---__J N 158 C NP l C 058

s======~~. TH232! NF lF ,p • .__ ______ __JU 8!NFlF ,p,

~=====:Jim~ IN115! l!N115M C: NP237!NFJf,p, NA23!NGlNA24

SC45!NGlSC46 ,__ __ __, PU239! NF lF ,p.

CU63!NGlCU64 U235!NFJf,p,

FE58!NGlFE59 MN55!NGlMN56 C059!NGlC060 AU197!NGlAU198

10 4-+~-+-~-+=-~+-~+-~i-----v~--1-~-+-~-l-~-+=-~+-~i------+~~~-+-~-1-~=<-~+-

o 2 4 6 8 10 12 14 1 6 1 8

ENERGY IN MEV


0. 5 - 1 .o 1 .ooo o.5 2.715E+08

1 • 0 - 1 ,5 1 .ooo 1 .o 1 .458E+08

1. 5 - 2.0 1 .ooo 1 ,5 8.709E+07

2. 0 - 3.0 1. 000 2.0 5.675E+07

3. 0 - 4,5 1 .ooo 3.0 2.555E+07

4 ,5 - 6.0 1 .ooo 4,5 7.539E+06

6 .o - 8.0 1 .ooo 6.0 2.094E+06

8.0-10.0 1 .ooo 8.0 5.914E+05

10.0-14.0 1 .ooo 10 .o 1 .919E+05

14.0- 18°0 1 .ooo 14. 0 1 • 207E +04

CHARACTERISTIC lNTEGRALS AVERAGED ACTIVITY OEVIATIONS

I, I z I 3 I 4 I 5 I s

10 4

ORIGINAL o.ooo o.ooo o.ooo o.ooo o.ooo o.ooo 9.32% 11.22% 9.32% 11°22%

FEW-GR. o.ooo o.ooo o.ooo o.ooo o.ooo o.ooo

MR. MCELROY, USR. REFERENCE-SPECTRUM

FIG. 65

1 o-10 1 0-9 10-8 1 o-7 · 1 o-6 1 0-5 1 o- 4 10-3 1 0-2 10-1 10° 101 102

1012 1012 -> w ::;:: '-

10 11+- /\ +ioll u w (j)

'-N llE llE 1010 +iolO ::;:: u 1 127 ( N2N l 1 126 0 '-z G24(NPJNR24 CJ - CJ

z 10 9 CJ f109 O'\ - c:::J '° 0 '° .... X

c::::::::J

::::J S32(NPJP32 c::::J

J-108

ö

- FE54(NPJMN54 c--=:J H

LL 10 6 N!58(NPJC058 C=:::J "'"' _J TH232(NFJF.P. er: U238(NFJF.P. - !Nl 15( NN J !Nl 15M t-z NP237(NFJF.P. c w 10

7 NR23(NGJNR24 \ 107 Cl::: SC45(NGJSC46 w PU239(NFJF.P. LL LL U235(NFJf.p. - CU63(NGJCU64 D 106 FE58(NGJFE59 \ +io

6

MN55(NGJMN56 C059(NGlC060

RU197(NGJRU198

1 05

1 1 1 1 1 1 1 1 1 1 1 ) 1 105

1 o-10 10-9 10-8 10-7 10-6 10-s 1 o-4 10-3 1 0-2 10-1 1 0° 101 102

ENERGY IN MEV

MR. MCELROY. USA. REFERENCE-SPECTRUM

CH. T.IBIXNER

KF A JÜLICH, 'NEST GEJ.1.'IANY

METHOD:

110

!I:he neutron apeotrum. ahould be approxima.te4 b7 the follow

ing seriea e.xpresaion m

1.) 'f (E) • lt f'o (E) (1 + > Ci 'f o (E) "1 (E)) l____i

ia1

where ':f (E) means a firat appro::idmation ot the sp~ctrwn, 0

a nor.malizing facto~,aithe di!f erential cross aections

of the m threehold detectors an.d c1 the coe!fioienta

to dete:rmined. !he7 are asoertained b7 minimjz~ th•

f ollowiD&

the proper, but unmow neutron apectrw:1„ When

dif!erentiating Q with respeot to c1 one obtail:la

:m.

3. > ) 111 'f.,, dE • lt ) 111 "o + k )~ 01 ~ r~ 0 1 111 ° 1·1

111

!?he firat appro:ximation <f 0

(E) ia selected out of a aet

of about 'O funotiolUI. !hie :tunotion ia uaed, vhere the

scatterilli cf the •peotral. indicea around their avarage

value 1• the am.alleat • • - 1["'1 5„) R • - -4*

8 -'Ai 1•1

A1 meana the act!vation (•aturated activitJ' per

target atom) and Ar the activation calculated with one of

the 30 :funotions„ LJ(E) 111 oaloulated in equidistant in

tervaJ.s of 0,2 MeV3 the activat1on integral• range :trom

O to 20 MeV„ !he inf'luenaee cf th• errora of the croaa

11ection. and the acti vatione are taku into account l:?r a MOil'o-

C.ARLO computation, vhioh carried out b7 the follo~

_.„ .....

a) calculation of aotivations trom the :meaaured

values and their correapondill8 errora

b) calculation croas aectiona from the tabulated

va1ues aru11 their error•

o) aelection of th• first approxim&iion

4) cal.culation of 'f (E).

SPECTPA PROCESSED~ Io Spectrum ( 7 results, Fig. 67 - 73 ).

IIo Spectrurn ( 6 results, Fig. /4 - 79 ). In the different. runs different detectors have been used „

11 2

REPTIESENTATION MOD.:; OF TEE RESULTS: 50-group spectra with

0.2 MeV group width.

ENERGY h_c_;GI ON : 0 „ 2 - 1 0. 2 MeV

GUESS SPECTRUTvl LIBRARY: Yes

RE~,IARKS: The cross section set seerns to be incorapt:iti ble „

113

0 2 4 6 8 1 0 12 1 4 1 6 18

1 o11 1 Ü II

> w :L

" u 1010 w (J)

" N

* * 1 09

1 09

:L u

" z

z 1 06

1 0 6

X ::::J _J

LL 1 0 7

107

_J

IT RL271NHEINR2 FE 61NPIMN56

f-z TI461NPI C46

1 06

1 06 w FE541NPIMN54

Q'.'. Nl581NPIC058 w LL INI151NNllN115M LL NP2371NFIF.P. ~ 0

105

105

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV

ENERGY GROUP FLUX/REF. FLUX ENERGY INTEGRRL FLUX

0. 5 - 1. 0 o.934 0.5 2.665E+10 l .o - 1 . 5 1 . 281 1 .o 1.933E+10 1 . 5 - 2.0 1 . 459 1 .5 1.370E+10

2. 0 - 3.0 1. 074 2.0 9.055E+09 3. 0 - 4,5 o.503 3.0 4.230E+09 4 • 5 - 5.0 1 . 609 4 ,5 2°479E+09 6 .o - 8.o 0.956 6.0 5.554E+Q8 5.0-10.0 1 . 164 8.0 1. l 86E+08

10.0-14.0 0 .137 10 .o 5.684E+06

14.0-18°0 14. 0

CHRRRCTERIST IC INTEGRRLS RVERRGED RCT!VlTY DEVIRTlONS

l 1 I 2 1 3 1 4 1 5 16 R1 R2 R3 R4

ORIGlNRL 0.137 o.065 0. 168 0°083 % 19. 87% 7.59% 7.59%

FEW-GR. 0. 120 0.049 0. 150 0°064

~1R. ME D NER. WES 1 ·GERMPNY. SPEC TRUM -

FIG. 67

> w :L '-. LJ w (j)

'-. N

* * :L LJ '-. z

z

X :::l _J

LL

_J

CI

fz w O::'. w· LL LL

0 2

114

4 6 8 10 12 14

~ RL27l NHE INR24 ~

~-------~ FES (NP 1 MN56 ~--------___, TJ46lNPI C46

~---------~ Nl58lNPJC058 ~. ~-------~ IN115lNNllN115M "· ~-------~ NP237( NF IF ,p.

1 6 1 8

1010

1 06

D 105'----f.Jl..--l-~-!----4r---+~--+-~-+-~t----l-~-!-~+i-~+---l~-l-~-l-~+---l~-"'l-~4-105

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o o.795 0.5 2.557E+IO 1 . 0 - 1 ,5 1 . 237 1 . 0 1 .934E+IO 1 . 5 - 2.0 1 . 468 1 ,5 1 .390E+IO 2. 0 - 3.0 0.938 2.0 9.229E+09 3. 0 - 4,5 0.835 3.0 5°014E+09 4 . 5 - 6.0 1 . 240 4 . 5 2 .108E+09 6. 0 - 8.o 1 . 1 1 4 6.0 6.256E+Ö8 5.0- 10.0 1 . 157 8.o 1. l 70E+08

10.0- 14.0 0. 113 10.0 4.702E+06 14.0-18.0 14. 0

CHRRACTERISTIC INTEGRALS AVERRGEO ACTIVJTY DEVIRTIONS

l 1 12 13 l4 l 5 16

ORIGINAL 0.051 o.076 0.054 0.085 % 18.05% 6.65% 6.65%

FEW-GR. 0.038 0.057 0.042 0.069

MR. MEIXNER. NE5T-GERMRNY. 5PECTRUM - 2

FIG. 68

> w L:

' LJ w ())

' N )IE )IE

L: LJ

' z

z

X :::) _J

lL

_J

CI

1-z w 0::: w lL lL

0

115

2 4 6 8 10 12 1 4 1 6 1 8

1 0 10

.___ _____ _____, AL27! NHE lNA24 .__ _______ _J FES ! NP lMN56

.___ ________ ___, T 146 ! NP l C 4 6

'--------------' N 158 ! NP l C058 .___ _______ ___, NP237! NF lF ,p.

D 10 5·-+'~-1-~+---1c----t-~-t-~+-~t---+~-+-~+i-~t----+~-+-~-+-~+-__,~-+~-+-10 5

0 2 4 6 8 10 12 14 16 18

ENERGY 1 N MEV


0 .s - 1 .o 0.902 o.s 2.548E+IO

1 .o - 1 .s 1 . 264 1 .o J .841E+IO

1 . 5 - 2.0 1 . 236 1 .5 1 .286E+IO

2. 0 - 3.0 0.830 2.0 8.923E+09

3. 0 - 4,5 0.900 3.0 5. J 94E+09

4. 5 - 6.0 1. 210 4,5 2.06!E+09

6 .o - 8.0 1 . 084 6.0 6.!44E+08

8.0-10.0 1 . 182 8.0 1. [ 94E+08

10.0-14.0 0. 113 10. 0 4.672E+06

14.0-18.0 14. 0

CHARACTER 1ST1 C INTEGRALS AVERAGEO ACTIVITY OEVIATIONS

l 1 l 2 1 3 14 l 5 l s

ORIGINAL 0.035 0.043 0.034 0.042 % 17.60% 7.09% 7.09%

FEN-GR. 0.027 0°027 0.025 0.028

FIG, 69

116

0 2 4 6 8 10 12 1 4 1 6 18 10 11 1 o11

> w :L -...... LJ 1 0 10

w (f)

-...... N )1( )1(

1 09 1 0

9

:L LJ -...... z

z 1 0 6 1 0 8

X ::::l __J

LL 10 7 107

__J

0:

27(NHEINR24'~ 1-z RL w 1 0 6 FES (NPIMNS6 ,~ 1 0 6

0:::: Tl46(NPJ C46 w "' LL NJS8(NPJCOS8 " ~" LL 1N1 1 S ( NN 1 1 N ! ! SM

b 1 05 "' 1 0

5

0 2 4 6 8 10 12 1 4 16 18

ENERGY 1 N MEV


0. s - 1 .o o.790 o.s 2.SS2E+IO 1 . 0 - 1 . s 1 . 278 1 .o ) .933E+IO 1 . s - 2.0 1 . 4 1 0 1 . s t .37!E+IO 2. 0 - 3.0 o.919 2.0 9.22SE+09 3. 0 - 4 . s o.867 3.0 S.098E+09 4 . s - 6.0 1 . 228 4 . s 2.078E+09 6. 0 - 8.0 1 .077 6.0 6. 1 1 OE +08 s.0-10.0 1. t 77 8.0 !.!90E+08

10.0 14. 0 0. 11 S 10.0 4.784E+06 14.0-18.0 14. 0

CHRRRCTER 15 T 1 C INTEGRRL5 RVERRGEO RCTIV!TY DEVIRTION5

1, l 2 1 3 1, l 5 l 5 R1 R2 R3 R,

OR!G!NRL 0.046 0.081 0. 041 0.086 % 17.94% s. 46% s. 46%

Frn-GR. 0.035 0.058 0.031 0.069

m<. ~1tJX~~l.r<. w=:sT-GERMRN:. SPECTRUM - 4

FIG. 70

117

0 2 4 6 8 10 12 14 16 18 10 11 1Ü11

> w L: '-. LJ 1010 w (j)

'-. N

* * 1 09

1 0 9 L: LJ '-. z

z 1 0° 1 08

X ::J _j

LL 107 10 7

_j

CI

AL 7lNHElNA24 f-z FE 6lNPJMN56

1 0 6 l 0 6 w TI46lNPl C46

"' Q'.'.

"' w ' LL 1N115[ NN l 1Nll5M LL NP237lNFJF.P.

D l 0 5 ' 10 5

0 2 4 6 8 l 0 12 1 4 16 18

ENERGY 1 N MEV


0. 5 - 1 .o o.790 o.5 2.605E+l0 1. 0 - 1 . 5 1 . 330 1 .o 1 .987E+10 1 . 5 - 2.0 1 .728 1 . 5 1 .4Q2E+l0 2. 0 - 3.0 Q.953 2.0 8.514E+09 3. 0 - 4,5 o.540 3.0 4.234E+09 4. 5 - s.o 1 . 499 4 . 5 2.356E+09 6 .o - 8.o o.971 6.0 5.640E+08 8.0 10.0 1 . 187 8.0 1 .205E+08

10.0- 14.0 0 .128 10. 0 5.324E+06 14.0-18.0 14. 0

CHARACTERISTlC lNTEGRALS AVERAGEO ACTlVITY OEVIATJONS

11 1 2 1 3 1 4 15 16 Al A2 A3 A4

ORIGINAL 0. 148 0. 139 0 .158 0. 187 % 19. 83% 8.01% 8.01%

FnJ-GR. 0. 11 7 0 .106 0. 1 38 0. 152

nR. ME;!Nt~. Wt5T-GERMRNY .. SPECTRUM 5

FIG. 71

> w :L

" (__)

w (/)

" N

* * :L (__)

" z

z

X ::::l _J

LL

_J

CI

fz w et:: w LL LL

0

1010

118

2 4 6 8 10 12 14 16

~------ AL271 NNE::: ~------~ FE5 l NP lMN~~A 24 ~ ~====================:J N 158 ( NP l C 05 8 ~

IN115lNNllN115M '"'-. ~----------' NP237l NF IF ,p. "'-, ·,

18

1010

D 10 5-t-J'---l---1--4--1---4--1-~-l---l-~-1--,µ_..-4~-1---1---l---1--4--"''----*-10 5

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o 0.840 o.5 2.511E+IO

1 . 0 - 1 ,5 1 .107 1 .o l.B53E+IO 1 . 5 - 2.0 1 . 21 4 1 ,5 1 .366E+IO

2. 0 - 3.0 1 .074 2.0 9.796E+09

3. 0 - 4. 5 0.902 3.0 4 .972E+09 4. 5 - 6.o 1 .005 4 ,5 1 ,ß31E+09

6. 0 - 8.0 1 .122 6.0 6.301E+08

8.0-10.0 1 • 164 8.0 l.176E+08

10.0-14.o 0. 111 10.0 4 .600E+06

14.0-18.0 14. 0

CHARACTER l ST l C lNTEGRALS AVERAGEO ACTIVITY DEVIATIONS

11 l 2 1 3 1, 15 l 5

ORIGINAL 0.021 0.031 0.023 Q.028 % 17.93% 7.00% 7.00%

Fu-J-GR. 0. 015 0.022 0.016 0.022

MR. MEJXNFR. WFST-GERMr:l~JY. SPECT.~U."'! - E

FIG. 72

119

0 2 4 6 8 10 12 1 4 16 18

1011 1 0 II

> w :L '-LJ 1010 w Cf)

'-N

* * 1 09

1 09

:L LJ '-z

z 1 06

1 06

X :::J _J

LL 10

7 10

7

_J

a: RL27!NHEJNR24

f-z FES !NPIMN56

1 06

1 06 w FE541NPJMN54

0::: Nl581NPJC058 w LL !Nl 151NN1!Nl15M '" LL NP2371NFJf ,p, ~ D 1 0

6 ~ 10

6

0 2 4 6 8 1 0 12 1 4 1 6 18

ENERGY IN MEV

E NE R GY GROUP FLUX/REF. FLUX ENERGY INTEGRAL FLUX

0. 5 - 1 .o 0. 841 o.s 2.539E+l0 1 . 0 - 1 .s 1 .135 1 .o 1.880E+l0 1 . 5 - 2.0 1 . 264 1 .s 1.381E+l0 2. 0 - 3.0 1. 080 2.0 9.788E+09 3. 0 - 4.5 0.883 3.0 4 .938E+09 4. 5 - 6.0 1 . 022 4 .s 1 . 865E +09 6. 0 - 8.0 1 .158 6.0 6.440E+08 8.0-10.0 1 . 140 8.o 1. 152E+08

10.0-14.0 0. 109 10.0 4.534E+06 14.0-18.0 14. 0

CHRRRCTERlST!C lNTEGRRLS RVERRGEO RCT!VlTY DEVJRTJONS

I 1 1 2 I 3 1 4 I s I s R1 R2 R3 R4

ORJGJNRL o.023 0.035 0.024 o.034 % 17.99% 6.62% 6°62%

FEW-GR. 0.018 0.026 0.0]9 0 .027

MR. ME!XNER. WEST-GERMRNY. SPECTRUM - 7

FIG. 73

120

0 2 4 6 8 10 12 1 4 16 1 8 1 0 9 10 9

> w l:: ....... u w 1 Oe 1 Oe (f) ....... N

)IE )IE

l:: u

10 7 ....... 10 7

z

z

X 1 0 6 1 0 6

:::J _J

LL

_J

a:

f-1 0 5 1 0 5

z NPlMN56 w 0::: w LL !NI 151 N LL NP237!Nflf.

D 10 4 10 4

0 2 4 6 8 1 0 12 1 4 16 18

ENERGY IN MEV


0. 5 - 1 .o 0.989 o.5 2.960E+08 l . 0 - 1 . 5 1 . 402 1 .o 1. 7 l 6E+08 l ,5 - 2.0 0.994 1 . 5 8.934E+07 2 .o - 3.0 o.936 2.0 5.920E+07 3 .o - 4,5 1 . 326 3.0 3.000E+07 4 ,5 - 6.0 o.&74 4,5 6.106E+06 6 .o - 8.0 o.539 6.0 !.345E+06 8.0-10.0 1 .297 8.0 5.361E+05

10.0-14.0 0.099 10 .o 1 . 775E +04 14.0-18.0 14 .o

CHARACTERISTIC INTEGRALS RVERAGEO RCTIVITY OEVIRTIONS

!1 l 2 l 3 l 4 l 5 l 5 R1 Rz R3 R4

ORIGINAL o. J 77 0. 105 0, J J 4 0. J 42 21 . 00% 7. 46% 7.46%

FEW-GR. 0.092 0.028 o.084 o.037

MR. MEIXNER. WEST-GERMANY. SPECTRUM 1

FIG. 7 4

121

0 2 4 6 8 1 0 12 1 4 1 6 18 10 9 109

> w :L '-... u w 1 0 8

1 0 8 (f)

'-... N

* * :L u

107 '-... 107 z

z

X 10 6 1 0 6

=> _J

LL

_J

CI:

f-10 5 10 5

z 7!NHElNA24 w FE54!NPlMN54 Q:'. Nl5B!NPlC058 w LL !Nl 15!NNl!Nl 15M LL NP237!NFlf ,p,

D 104 1 0 4

0 2 4 6 8 1 0 12 14 1 6 18

ENERGY 1 N MEV


0. 5 - l .Q l .083 Q.5 2.917E+OB l . 0 - l ,5 l .087 l ,Q l . 554E +OB 1 . 5 - 2.0 Q.985 l ,5 9 .163E+07 2. 0 - 3,0 l ,[39 2.0 ö.173E+07 3. 0 - 4,5 1 .007 3,Q 2.61BE+07 4. 5 - 6.Q 1 . 048 4,5 B.035E+06 6 ,Q - a.o 1 .278 6.Q 2.330E+06 a.0-10.0 Q.982 a.o 4.106E+05

10.0-14.0 0, [ 01 10.0 l . B20E +04 14.0- 18.Q 14. 0

CHARACTERlSTIC INTEGRALS AVERAGED ACTlVITY DEVIATIONS

11 12 I 3 1 4 l 5 l 5 A1 A2 A3 A4

ORIGINAL o.037 0.019 0.037 0.025 22.29% 7.64% 7.64%

FEW-GR, 0.019 Q,QQ7 0.018 Q,QQ7

MR. ME!XNER. WEST-GERMRNY. SPECTRUM 2

FIG. 75

122

0 2 4 6 8 10 1 2 14 16 18 1 0 9

109

> w L: -....._ LJ w 1 0 8

1 0° (/) -....._ N

* * L: LJ

10 7 10

7 -....._ z

z

X 1 0 6

106

:::J _J

lL

_J

0:

f-10 5 1 0 5

z w et:: RL27!NHE R24 w lL Nl58!NPJC058 lL IN115!NNl!N!l5M

0 10 4 10 4

0 2 4 6 8 10 1 2 14 16 18

ENERGY IN MEV


0 .5 - 1 .o 0.206 o.5 1 .641E+08 1 . 0 - 1 ,5 o.593 1 .o 1 .383E+08 1. 5 - 2.0 1 . ! 57 1 ,5 1 .035E+08 2 .o - 3.0 1 . 362 2.0 6.839E+07 3 .o - 4,5 o.989 3.0 2.590E+07 4. 5 - 6.0 1 .008 4,5 8.093E+06 6. 0 - 8.0 1 . 4 41 5.0 2.603E+06 8.0-10.0 1 .058 8.0 4.375E+05

!0.0-14.0 0.082 10.0 1 .475E+04 }4.0-18.0 14. 0

CHARACTERISTIC INTEGRALS AVERAGED RCTIVITY DEVIATIONS

11 l 2 13 !4 l 5 15 Rl Az A3 R4

ORIGINAL 0.} 07 o.553 0.088 0.227 25 · 14% 5. 15% 5.} 5%

FEW-GR. 0.099 0.512 o.088 0.253

MR. MEIXNER. WE5T-GERMRNY. 5PECTRUM 3

FIG. 76

123

0 2 4 6 8 10 1 2 1 4 16 1 8 1 0 9

10 9

> w l:: ....... u w 10 8

10 8 (/) ....... N

* * l:: u

1 0 7 107 .......

z

z

>< 1 0 6

106

~ _J

LL

_J

0:

1-1 0 5 1 0 5

z w O::'. 24 w LL Nl58!NPlC058 LL NP237!Nf lf,p,

0 104

10 4

0 2 4 6 8 1 0 1 2 1 4 16 1 8

ENERGY 1 N MEV

ENERGY GROUP FLUX/REF. FLUX ENERGY lNTEGRRL FLUX

0. 5 - 1 .o 0.787 o.5 2.983E+08 1 . 0 - 1 ,5 1. 382 l . 0 1 .994E+08 1 ,5 - 2.0 1. 739 1 ,5 1 .183E+08 2 .o - 3,0 1 . 303 2.0 6.559E+07 3 .o - 4,5 0.902 3.0 2.492E+07 4. 5 - 6.0 1 .087 4,5 8.679E+06 6 .o - 8.0 1 .558 6.0 2.762E+06 8.0-10.0 1 .023 8.0 4.215E+05

10.0-14.0 0.072 10 .o 1 .296E+04 14.0-18.0 14 .o

CHRRRCTERlSTlC lNTEGRRLS RVERRGED RCTlVlTY OEVlRTlDNS

11 l 2 l 3 l4 l s l s R1 R2 R3 R4

ORlGlNRL 0. 136 0. 136 0. 167 0. 127 28.74% 9.50% 9.50%

FEW-GR. 0 .117 0°085 0. 157 0.091

MR. MEIXNER. WEST-GERMRNY. SPECTRUM 4

FIG. 77

124

0 2 4 6 8 10 1 2 14 1 6 18

1 0 9 10 9

> w :c ......_

LJ w 1 0 8 10 8

(/) ......_

N )!(

* :c LJ

10 7 ......_ 10 7

z

z

X 1 0 6 10 6

:::J _J

LL

_J

<I

f-1 0 6 10 5

z w AL 27( ElNA24 a::: NI58(NPlC058 w LL IN115(NNlIN115M LL NP237(NFJF.P.

0 1 04 10 4

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV ·ft


0. 5 - 1 .o 1 .036 0.5 2.989E+OB 1 . 0 - 1 ,5 1 . 352 1 .o 1 . 687E +OB 1 . 5 - 2.0 1. 177 1 ,5 8.939E+07 2. 0 - 3.0 0 .8(,3 2.0 5.370E+07 3 .o - 4,5 1. 042 3.0 2.865E+07 4. 5 - 6.0 1 . 323 4,5 9.884E+06 6. 0 - 8.0 1 .509 6.0 2.679E+06 e.0-10.0 o.993 8.0 4.120E+05

10.0-14.0 0.085 10 .o 1 . 528E +04 14.0-18.0 14. 0

CHARACTERISTlC INTEGRALS AVERAGED ACTIVITY DEVIATIONS

11 12 1 3 14 I 5 16 A1 Az A3 A4

ORIGINAL 0 .104 o.061 o.098 0.075 23. 53% 8.38% 8.38%

FEW-GR. 0.084 o.024 o.085 0.028

MR. MEIXNER. WE5T-GERMRNY .. SPECTRLJM 5

FIG. 78

125

0 2 4 6 8 10 12 14 16 18 l0 9-t-~-J---1r--r~-t--~t--+~-+-~-1---1~-1-~+---l~-l-~4-~l----l-~-+-~.j....-10 9

> w l::

' u w (f)

' N

* * l:: u

' z

z

X ::> _J

LL

_J

CI

rz w Cl::: w LL LL

1 0 5 c:=====~5:LJAL27! NHE lNA24

~--------TI 46( NP lSC '--------------' FE54 ( NP l HN54 '-----------'NI 58! NP lC058

'------------' IN115!NNlIN115H ,__ _____ ___, NP237! NF lF ,p.

1 0 6

1 0 5

D 10 4-+'~-+-~+---;~-+~-+-~-1-~1---+~-+~+i-~t---+~-+---'-+-~+---i~-+~-+- 10 4

o 2 4 6 8 10 12 14 16 1 8

ENERGY IN MEV


0 ,5 - 1 .o 1 .079 Q.5 3.009E+08 1 .o - 1 ,5 1 . 296 1 .o 1 .652E+08 1 . 5 - 2.0 1 .171 1 ,5 8.924E+07 2. 0 - 3.0 1 .015 2.0 5.370E+07 3 .o - 4,5 o.545 3.0 2.202E+07 4 ,5 - 6.Q 1. 738 4,5 1 .220E+07 6 .o - 0.0 1 .583 6.0 2.735E+Ö6 0.0-10.0 o.841 0.0 3.566E+05

10.0-14.0 0. II 4 10.0 2.052E+04 14.0-18°0 14. 0

CHARACTERISTIC INTEGRALS AVERAGED ACTIVITY OEVJATIONS

11 I 2 I 3 I4 l 5 l 5

ORIGINAL 0 .320 0.040 0.404 0.053 22.98% 7.64% 7.64%

FEW-GR. 0.202 0.022 0°237 Q.024

MR. Mf!XNER. WEST-GER~~NY. SPECTRUM 6

FIG. 79

126

J „ MOHIN, J • DORLET

CEA PARIS, .2FANCE

METHOD:

C 1est la methode suggc;ree dans Particle de W. N. Mc ELROY, S. BERG et G, GIGAS (N. S. E. 27-533-541 (1967) ), sous la forme la plus simple possible :

- etant donnce une rcpresentation multigroupe ~i (y) des scction efficaces des I detecteurs utiliscs sur les J groupes, on part d 1unc clensit de flu~nce positive arbitraire ß (y) et on ca_lcule les taux de reaction:

J AC (i) = i=l J6 (y) ~i (y)

On modifie ensuite la densite de fluence en prenant :

i:_ A(i) i = l AC ( i} p ( y ) t;"i ( y )

I i~ ~i (y)

ou les A(i) sont les taux de reaction mesures, et on itere le procede.

Si les A(i) sont compatibles, on obtient une densite de fluence repondant a la question posee.

Sinon on essaie drextraire de la serie de detecteurs utilisec unc sous-seric. compatible maxi male et c 1est a partir de cette serie que l'or. determine le spectre cherche.

Toutes les compatibilites ci-dcssus s'entendent sur les taux de reactions donnes, sans utilisation des marges d'errcur experimentales. En effet, le probleme est su!fisammem sous dctermine pour que les incompatibilites observees soient significatives.

1 2?

SFSCI'RA PROCESSED: r„ Spectrum ( 3 results )

I. 1 „

I.2. I„3„ II„1 „

II„ Spe et rum I' 2 results ) \

JV!iniwal flux ( Fig. 80 and 81 0 )

Average flux /' Fig„ 82 and 83„ ) \

Maximal flux I' Fig ... 84 and 85„ ) \

( Fig. 86 and 87„ ) and II ... 2 I' Fig 88„ and 89„ ) - Two \

spectra using the same method and the same 8 threshold

dJtectors; in the II.1. additionally the U235(NF)FeP„,

in the II.2. additionally the PU239(NF)F.P. reaction

was used.

REPRESENTATION MOD.~. OF THE RESULTS: 37-group fluxes

ENERGY REGION: 0.0 - 11.0 MeV„

GUESS SPECTRUM LIBG.ARY: No

RE?>J:ARKS: The thermal and epithermal neutrons are represented only by 2 groups below 0„01 MeV„

128

0 2 4 6 8 10 1 2 1 4 1 6 18 1011 1011

> w :I:: '-. LJ 1010 w (f)

'-. N

* * 109 109 :I:: LJ '-. z

z 1 06 106

X =:)

_J

lL. 10

7 10

7

_J

er: FE54(NPlMN54 NI58(NPlC058 r-

z U238(NFJF.P. 1 0

6 10

6 w IN115(NNlIN115M O::'. NP237(Nf Jf ,p, w lL. PU239(NFJf,p, lL. U235(NFJf ,p,

0 10

5 10

5

0 2 4 6 8 10 12 1 4 16 18

ENERGY IN MEV


0. 5 - 1 . 0 0.077 0.5 2.063E+l0 1 . 0 - 1 ,5 1 .551 1 .o 2°003E+l0 1 . 5 - 2.0 1 . 428 1 ,5 1 .321E+l0 2. 0 - 3,0 0.808 2.0 8.662E+09 3. 0 - 4. 5 0.812 3.0 5°034E+09 4. 5 - s.o 1 . 369 4,5 2.209E+09 6 .o - 8.0 0.903 6.0 5.731E+08 9.0-10.0 1 . 166 B.O 1 .606E+OB

10.0-14.0 1 . 143 10 .o 4. 743E+07 14.0-18.0 14. 0

CHRRACTERISTIC INTEGRALS RVERRGED RCTIVITY DEVIATIONS

I 1 1 2 1 3 I4 I 5 I 5 A1 Az R3 A4

ORIGINAL 0.252 Q.732 2.58E+6 0. 454 D ,977 7.31E+6 26.92% 12.93% 8.82% 4. 25%

FEW-GR. 0. 109 o.574 l.28E+6 0.101 Q.274 4 .27E+6

M~S. MORIN RND MR. DORLET. FRRNCE, SPECTRUM MINI

FIG. 80

i o-10 10-9 10-8 10-7 10-6 10-5 1 o-· 10-3 1 o-z 1 0-1 10° 101

1 02

1011 1 011 ~

> w L: '-u

10 14 1 1 / ~I +1010 w

(/)

'-N ll: ll: L: u 109

.._. 109

'-z -z .....

°' ~

M CO

C\l ..- X 1 0

8 10

8 0 ::::) H _J i:x.. LL

_J

a: ~

107 vv

-l-101

1-z MG24CNPINR24 w RL27CNHEINR24 q 0::: FE56CNPJMN56 D w

FE54CNPJMN54 c:::::::J LL LL Nl58!NPJC058 c::::::J ~ 106 U238!NFJF.P. c::=J 1\ +10

6 0

INllSCNNl!N!!SM c::=:::J NP237CNFJF.P. c::=J

PU239!NFJF.P. U235!NFJF.P.

10

5

'

! 1 1 1 1 1 1 1 1 1 1

11 \

' 105

i o-10 10-9 10-8 1 0-1 1 o-6 1 o-5 1 o-• 10-3 1 o-z 10-1 10° 101

102

ENERGY IN MEV

MRS. MORIN RNO MR. DORLET. FRRNCE. SPECTRUM MINl

130

0 2 4 6 8 1 0 12 1 4 16 1 8 10 11 1011

> w l:::: ......_

LJ 1010 w (f) ......_

N

* lli 10 9 10 9 l:::: LJ ......_

z

z 1 ÜB 1 ÜB

X ::J _J

LL 107 AL2 ( 1 0 7

_J FE56 (NP l a:: FE54!NPJMN54

1-NI56!NPIC056

z U236!NFJf,p, 106 10 6

w IN1!5!NNJIN115M n::: NP237!NFJf ,p, w LL PU239!NFIF.P. LL U235!NFJf,p,

0 10 5 10 5

0 2 4 6 8 10 12 14 16 18

ENERGY 1 N MEV


0. 5 - 1 .o 0.030 0.5 2.033E+l0 1 .o - l ,5 1 ,539 1 .o 2.0lOE+lO 1 ,5 - 2.0 l .569 l ,5 1 .333E+IO 2 .o - 3.0 o.746 2.0 6.339E+09 3 .o - 4,5 o.767 3.0 4.9BOE+09 4. 5 - 6.0 1 . 457 4,5 2.309E+09 6. 0 - e.o o.697 6.0 5.677E+OB e.0-10.0 l .164 e.o 1 .562E+06

10.0-14.0 l .044 10.0 4.332E+07 14.0-16.0 14 .o


l 1 I 2 l 3 1 4 l 5 I 6 Al Az A3 A4

ORIGINAL 0.297 o.637 l .06E+5 0.559 l .260 2.94E+5 14.64% 13.92% 6. 4 l % 4.55%

FEW-GR, 0. l 39 o.641 5.32E+4 0 o l 34 0.262 1 .69E+5

MRS. MOR!N RNO MR. DORLET. SPECTRUM m 1 m

FIG. 82

1 o-10 10-9 10-8 1 0-1 1 o-s 1 0-5 10-4 i o-3 10-2 1 0- 1 1 0° 10 1 102

1011 l oll

-> w L: ....___

u 10 1~ 1 ~I +10

10 w (f) ....___

N

* * L: u 109 / 1 1 \\ +10

9 ....___

z -z

>=j H

108t / ~1 /

~ tlOe ,,

X . ::J ! _,,

_J \..N ())

lL ......

V.J

_J

a: ~

107 vv D~ +107 f-

z MG24(NflNR24 w AL27(NHElNR24 D ()'.'.: FE56(Nf lMN56 D w FE54[NflMN54 c:=i lL lL Nl58(NflC058 C=::J ~ 106 U238[NFJF.f. c::=:::::J 1 1 +10

5

0 IN115[NNl!N115M c::::::=::J NP237[NFJF.f. c::::=:i

PU239[NFJF.P. U235[NFJF.f.

105

1 !

1 1 1 1 1 1 1 1 1 1 ,11

1 105

1 o-10 1 o-9 1 0-0 10-7 10-6 10-5 1 o-4 10-3 1 0-2 1 0-1 10° 101 102

ENERGY IN MEV

MRS. MORIN RNO MR. OORLET. SPECTRUM * 1 *

1 o-10 10-9 1 o-8 10-7 1 o-s 1 0-5 1 o-4 10-3 10-2 1 0-1 10° 101 102

10111 1 1 1 1 1 1 1 1 1 1 1 1

1011

~

> w L: -...... u

10 1~ 1 'il +iolO w (f)

-...... N

* * L: u

1 0 9 / l 1 ~ +io9

-...... z ~

~ z H 0 . !O't / 'J\ ~} \ t!O' X CD ::)

~ .+::- _J \..>! LL 1\)

_J

a:: ~

107 vv d +io7 ..__

z MG24CNPJNA24 w AL27CNHEJNA24 d Q:'. FE56CNPJMN56 CJ w FES4CNPJMN54 c=:J LL LL NIS8CNPJC058 c:::=J ~ 106 U238CNFlf .P. ~11 +ios 0 INl!SCNNJIN!ISM c::::==i

NP237lNFlf.P. ~ PU239lNFlf.P.

U23SlNFJf.P.

105 ' I

1 1 1 1 1 1 1 1 1 1 ,11 1 105

1 o-10 10-9 10-8 1 o-7 1 o-6 1 o-5 1 o-4 1 o-3 10-2 10-1 1 0° 101 102

ENERGY IN MEV

MR5. MORIN RNO MR. OORLET. FRRNCE. 5PECTRUM MRXl

133

0 2 4 6 8 1 0 12 1 4 1 6 1 8 1011 1011

> w :L '-..

1 0 10 LJ w (f)

'-.. N

* * 10 9 10 9

:L LJ '-.. :z

:z 1 0 8 10

8

X ::J _J

LL 10 7 1 0 7

_J

a: FE54!NPlMN54 NJ58!NPlC058

1--:z U23B!NFlf,p,

1 0 6 10 6 w !Nl 15( NN l 1Nl 15M 0::: NP237!NFlf ,p, w LL PU239!Nf )f,p, LL U235!NF)f,p,

D 10 5 10 5

0 2 4 6 8 10 12 14 16 1 8

ENERGY IN MEV


0. 5 - 1 .o 0.055 o.5 2.035E+l0 1 .o - 1 ,5 1 . 517 1. 0 1 .992E+10 1 . 5 - 2.0 1 . 435 1 ,5 1 .325E+l0 2. 0 - 3,0 0.810 2.0 B.679E+D9 3 .o - 4,5 0.814 3.0 5.041E+09 4 ,5 - 6.0 1 . 366 4,5 2.206E+09 6 .o - s.o 0.904 6.0 5.739E+OB s.0-10.0 1. 166 s.o 1 .607E+OB

10.0-14.0 1 .146 10.0 4. 754E +07 14.0-18.0 14. 0

CHARACTERISTIC INTEGRALS AVERAGED ACTIVITY OEVJATIONS

l 1 l 2 1 3 l 4 l s l s Al R2 A3 A4

ORIGINAL 0.260 o.767 8.25E+4 0. 464 1 . 048 2.24E+5 13. 61 % 12. 91 % 6 .11 % 4. 31 %

F EW-GR. 0 .109 o.592 4.0BE+4 0.093 Q.242 1 .29E+5

MRS. MnRIN ~NO MR OORLET. FRRNCE. SPECTRUM Mnx1

FIG. 85

134

0 2 4 6 8 1 0 12 1 4 1 6 18 10 9 109

> w :L '-.. LJ w 10 8

10 8 ([)

'-.. N )1(

)1(

:L LJ

10 7 '-.. 1 07

z

z

X 10 6 106 ::J

__J

LL MG24!NPlNA24 __J AL27!NHElNA24 CI FE56!NPlMN56

f-10 6

54 z 05 10 6

w U23 O::'. w LL LL

D 10 4 104

0 2 4 6 8 1 0 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o o.692 o.5 2.435E+06 !. 0 - 1. 5 1. 036 1 .o 1 .565E+06 1 . 5 - 2.0 1 .122 1 ,5 9.562E+07 2. 0 - 3.0 1 . 040 2.0 6 .159E+07 3 .o - 4,5 1 .220 3,0 2.914E+07 4. 5 - 6.0 1 .066 4,5 7 .160E+06 6. 0 - 6.o o.435 6.0 1 .357E+06 6.0-10.0 1. 700 6.o 7.032E+05

10.0-14.0 0. 133 10.0 2.367E+04 14.0- 16.0 14. 0


I 1 I 2 1 3 14 I 6 I 6 A1 Az A3 A4

ORIGINAL 1 .092 0 .109 3.264 3.636 o.099 6.571 26.36% 16. 32% 6.33% 4.74%

FEW-GR, 0 .165 o.073 o.610 0. 166 o.064 1 . 622

MRS. MOR!N. RNO. MR. OORLET, FRRNCE. SPECTRUM F!(PU5l

FIG. 86

1 o-10 10-9 10-8 1 0-1 10-6 10-s 1 o-4 1 0-3 10-2 1 0-1 10° 101 10 2

10121 1 1 1 1 1 1 1 1 1 1 1 1 1012 ~

> w ::;::

" 10 11-f- /\ +io11 u w Cf)

" N

* * 10 1~ ~ \ rv '--'I +io10 ::;:: {'-._

u

" z -z !OJ / \j \ ro· !.!'\ ~

!"\ t--.,... X CO :::J _J . LL 108 1 0°

ö H i::..

_J

a: ~

1-z

107+ HG24lNPlNR24 ~ 0 +io

7 w 0:::: w LL LL FE54lNPlHN54 ~ Nl58lNPlC058 0

1\1 +io6 10 U238lNFJF.P.

IN115lNNl!N115H c:::==::::::J NP237lNFJf.P.

U235lNFJF.P.

105

1 1 1 1 1 1 1 1 1 1 1 I~,

1 1 05

1 o-10 1 o-s 10-8 1 o-7 10-6 10-s 1 o-4 10-3 10-2 10-1 10° 10 1 102

ENERGY IN MEV

MRS. MORIN. RNO. MR. OORLET. FRRNCE. SPECTRUM Flf PU5l

> w ~ '-.. u w (/")

'-.. N

* * ~ u '-.. z

z

X :::J _J

LL

_J

a:

1-z w Q'.'.

w LL LL

0

136

MG24CNPlNA24 1..>...----1~ AL27 ( NHE l NA24

r--l------1-~ FE56C NP lMN56

i----~ PU239C NF lF ,p.

54 05

10 4..,...~-1-~--~1---+~-+~-l-"-~--~i--........ ~--~-1-~.i--.....j.~ .... ~--~.J-~1----1--10•

0 2 4 6 8 10 12 14 16 18

ENERGY GROUP

o.5- 1.0 1 . 0 - 1 ,5 1 ,5 - 2 .o 2.0- 3.0 3.0- 4,5 4,5- 6.0 6.0 - 8.0 8.0-10.0

10.0 - 14.0 14.0-18.0

FLUX/REF. FLUX

0.778 1. 042 1 .116 1 . 039 1 .219 1 .069 0. 435 1. 700 0. J 33

CHARACTERIST!C INTEGRALS

ENERGY

o.5 1 .o 1 ,5 2.0 3.0 4,5 6.0 8.0

10 .o 14 .o

ENERGY IN MEV

INTEGRAL FLUX

2.544E+08 1 .565E+08 9.54!E+07 6. l 55E+07 2.914E+07 7. ! 78E+06 1 .356E+06 7.03!E+05 2.390E+04


ORIGINAL t.090 0.077 !.088

FEW-GR. 0.182 0.039 0.452

3,739 o.074 3.361

0.160 0.036 o.545 34.78% 18.33% s.21% 4.82%

~RS. MO~JN. RNO. MR. OORLET, FRRNCE. SPECTRUM FllUSl

FIG. 88

1 o-10 1 0-9 1 0-0 10-7 1 o-s 1 o-s 10-4 10-3 1 0-2 1 0-1 10° 101 102

10121 1 1 1 1 1 1 1 1 1 1 1 1 1012 ~

> w ::;::: .......

1011+- /\ +10

11 u w (f)

....... N

* * 1 0 1.Q.f- r \ )"V '-'-1 +1010 ::;::: /\..._

u ....... z ~

t- z !DJ / V \ ro· I<'\ -,,.... O'\ X Cl)

:::::> . _J

0 lL 108 108 H

~ _J

CL -1-z

101+ MG24CNPlNR24 ~ 0 +10

1 w 0::: w

10.l lL FE56CNPlMN56 lL FE54lNPlMN54 - Nl58lNPlC058 0

U238CNFJF.P. 1\1 +106

!Nll5CNNllN115M c:::::==l NP237lNFlf.P.

PU239lNFlF.P.

1 05 1 1 1 1 1 1 1 1 1 1 1 ld' l 105 1 o-10 1 0-9 10-8 1 0-1 1 o-6 1 o-5 10-4 10-3 10-2 1 0-1 10° 101 102

ENERGY IN MEV

MRS. MORIN. RNO. MR. DORLET. FRRNCE. SPECTRUM FlfU5l

138

M„ NAJZER

LJUBLJANA, JUG08LAVIJA

METHOD:

ITER 2 was developed originally. It is supposed that a first approximation 0

0(E) of the measured spectrum is known„

Then a sensitivity function, defined by

8~(E) 0( 00

(E) ~(E) i = 1, 2, „., n

where E stays for the energy, t1

for activation cross section of the ith detector and n for the number of detectors in the set, is calculated. The first correction 0 . is oalculated for each detector retaining the shape of 0 ~~ . = K .0 ,

S 0 0 01 01 0 K ~=Ai/ 81dE, Ai being measured specific activity of the i~ detector. The seoond approximation ~1 (E) is obtained by averaging ~OL weighted by sensitivity functions:

n n

01 (E) = L: 8~(E) ~oi (E)/ z:8~(E) i=1 i=1

The procedure is repeated by 01 , 02 , „ •• , 0k until diferences b.etween measured acti vi ties Ai and values of expressions ~ ~k(E) Vi(E)ld.E are in the range of experimental errors„

~ accomplish the intercomparison two modifications were made in ITER-2:

a)'l Numerical experiments on a number of test spectra showed that some kind of smoothing is necessary to prevent oscillations when large number of activation detectors are

involved in evaluation„ A Gaussian smoothing with ()= 0,7 MeV was therefore included in the programm. It was performed after the tenth and the last iteration on the calculated spectrum above neutron energy of MeV. ~elow this energy the smoothing due to the group width was considered sufficient„

b) The cross section library was extended and updated. Group cross sections were obtained by \T'(E) data and Watt•s fission spectrum. If necessary, data were renormalized to fit experimantal fission spectrum averaged cross sections

<&/ fiss" In this way two cross section sets marked 08-A and 08-B was generated.

139

SPEC~RA PROCESSED: I„ Spectrum ( 8 results )

II„ Spectrum ( 7bresults )

I.1. - I.6. ( Fig. 90 - 95. ) In all of these rnns 10 - 10 d2tectors were used in different sets ( set 1.,

2. and 3. ). In the runs I.1, I„3. and I.5 a cross section set called CS-A, in the another

runs the cross section set CS-B was used. I. 7. - I .8. ( Fig „ 96 - 97 „ ) Runs wi th 15 d3tectors using

the cross section set CS-A and CS-B respectively„

II„1 - II.6 ( Fig. 98 - 103. ) The same as by the I. Spectrun. II„7. ( Fig. 104. ) Run with 15 detectors using the CS-B

cross section set.

REPRESEl\TATION MODE OF THE RESULTS: 72-ppint differential spectrum.

ENETIGY REGION: 0 .O - 18.0 MeV ( Wi th threshold detectors only )

GUESS SPECTTIUM LIBRARY: No

REMARKS: Nm

140

0 2 4 6 8 10 12 14 16 1 8 1011 1011

> w L: "-._

1010 (__) 1010 w (f)

"-._

N

* * 1 09

1 09

L: (__)

"-._

z

z 108 10

8

X ::::J _J 11271N2N11126 LL 10

7 RL271NHEINR24 1 0 7

_J

CI S321NPIP32

r-- NJ581NPICD58 z FE541NPIMN54

10 6 10 6 w TH2321NFJF.P. D::: U2381NFIF.P. w LL IN! 151NN1!Nl15M LL NP2371NFIF.P.

D 105 10

5

0 2 4 6 8 10 12 14 1 6 18

ENERGY IN MEV


0. 5 - 1 .o 0.743 o.5 2.355E+10 1 . 0 - 1 .5 1 . 022 1 .o 1 .773E+10 1 . 5 - 2.0 0.964 1 . 5 1 .323E+10 2. 0 - 3.0 1 . 075 2.0 1 . 016E+1 0 3. 0 - 4.5 0.990 3.0 5.337E+09 4. 5 - 6.0 1 . 033 4,5 1 . 892E +09 6. 0 - 8.0 1 . 116 5.0 6.572E+08 8. 0 - 10.0 1 . 198 8.0 1 .476E+08

10. 0 - 14. 0 0. 725 10.0 3.134E+07 )4.0-18.0 0.906 14. 0 1 ·239E+06

CHRRRCTERISTJC JNTEGRRLS RVERRGED RCTIVITY DEVIRTJONS

11 12 1 3 14 1 5 1 6 R1 R2 R3 R4

ORJGJNRL 0.021 0.062 0.012 0.026 7.26% 6.88% 6.88%

FEN-GR. 0.015 o.039 0.008 0.023

. MR. NRJZER. JUGOSLRVJJR. SET 1. CS-R

FIG. 90

141

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 1Ü11 1Ü11

> w ::c '-...

1010 (__) 1 0 10 w (/)

'-... N

* * 109

1 0 9

::c (__)

'-... z

z 108

108

X ::::l _J 1127 ( N2N l 1126 LL 10

7 AL27(NHE1NA24 107

_J

0::

S32(NflP32 f-z NJ58(NflC058

1 0 6 1 0 6 w TH232( NF lF ,p. Q'.'. U238(Nflf,p, w LL JNJ15(NN11Nll5M LL NP237(Nf lf ,p,

0 105 1 0 5

0 2 4 6 8 1 0 1 2 1 4 16 1 8

ENERGY IN MEV


0. 5 - 1 .o 0 .9 J l o.5 Z.365E+10 1 . 0 - 1 . 5 1 . 038 1 . 0 1 .652E+10 1 . 5 - 2.0 o.647 1 . 5 1 .196E+10 2. 0 - 3.0 1 . 016 z.o 9.895E+09 3. 0 - 4 ,5 1 . 000 3.0 5.331E+09 4. 5 - 6.0 1 . 021 4,5 1 .849E+09 6. 0 - 8.0 1 .072 6.0 6.296E+08 8.0-10.0 1 . 123 8.0 1 .398E+08

10.0-14.0 o.712 10.0 3.078E+07 14.0- 18.0 0.919 14.0 1 .257E+06

CHARACTERISTIC INTEGRALS AVERAGED ACTJVITY DEVJATJONS

11 12 1 3 1 4 15 1 6 A1 Az A3 A4

ORIGINAL 0.026 o.082 0.021 0.066 6 .57% 7 .17% 7 .17%

FEW-GR. 0. 011 0.017 0.009 0.018

. MR. NRJZER. JUG05LRVIJR. 5ET 1. C5-B

FIG. 91

142

0 2 4 6 8 10 1 2 1 4 16 18 1011 1 Q II

> w ::C "- 1010 1010 LJ w (f)

"-N

* * 10 9 109

::C LJ

"-z

z 1 0 8 108

X :::J _J 1127( N2N 11126 LL 10 7 10

7

_J

CI

532(NPIP32 f--z Nl58lNPIC058

10 6 106

w FE54lNPlMN54 er: TH232l NF lF ,p. w LL U238lNFIF.P. LL. NP237lNFJF.P.

D 105 1 05

0 2 4 6 8 10 12 14 1 6 18

ENERGY IN MEV


0. 5 - 1 .o o.782 o.5 2.302E+!O 1 . 0 - 1 ,5 o.946 1 . 0 1 .690E+10 1 . 5 - 2.0 o.876 1 . 5 1 .274E+10 2. 0 - 3.0 1 .028 2.0 9.950E+09 3. 0 - 4.5 o.982 3.0 5.330E+09 4. 5 - 6.0 1. 045 4,5 1 .912E+09 6. 0 - 8.0 1 . 127 6.0 6.634E+08 8.0-10.0 1 .211 8.0 i .487E+08

10.0-14.o 0. 721 10 .o 3.115E+07 14.0-18.0 0.896 14. 0 1 .225E+06

CHRRRCTERl5TIC INTEGRRL5 RVERRGED RCTIVITY DEVJRTJON5

l 1 l 2 1 3 1 4 15 l s RI R2 R3 R4

ORIGINRL 0.023 0.047 0.018 0.025 7.35% 7.89% 7.89%

FEW-GR. 0.017 0.030 0 .011 0.020

. MR. NRJZER. JUGOSLRVIJR. SET 2. CS-R

FIG. 92

143

0 2 4 6 8 1 0 1 2 14 1 6 18 1011 1 0 II

> w :L "-- 1010 (__) 1 0 10 w (f)

"--N

* * 10 9

1 09

:L LJ "--:z:

:z: 108 108

X ::::J _J I 127( N2N 11126 LL

10 7

1 0 7

_J

a: S32tNPIP32

1-:z: NI58tNPIC058

1 06

1 0 6 w FE54tNPIMN54

Cl:'.'. TH232( NF IF ,p. w LL U238tNFIF.P. LL NP237tNFIF.P.

0 10

5 1 0

5

0 2 4 6 8 1 0 12 1 4 1 6 1 8

ENERGY IN MEV


0. 5 - 1 .o o.789 o.5 2°263E+l0 1 . 0 - 1 ,5 0.937 1 . 0 1 .645E+l0 1 . 5 - 2.0 o.848 1. 5 1 .233E+l0 2. 0 - 3.0 o.971 2.0 9.632E+09 3. 0 - 4,5 0.968 3.0 5 °272E+09 4. 5 - 6.0 1 . 054 4 ,5 1 . 903E +09 6 .o - 8.0 1 .096 6.0 6.431E+08 8.0-10.0 1 . J 52 8.0 1 .425E+08

10.0-14.0 o.710 10. 0 3°070E+07 14.0-18.0 0.909 14. 0 1 .243E+06

CHRRRCTERISTIC INTEGRRLS RVERRGED RCTIVITY OEVIRTIONS

l 1 12 1 3 1 4 15 16 R1 R2 R3 R,

ORIGINRL 0.015 o.046 0.013 0.026 6. 4 3% 7.01% 7. 01 %

FEW-GR. 0.o11 0.029 0.008 0.021

. MR. NRJZER. JUGOSLRVIJR. SET 2. CS-8

FIG. 93

144

0 2 4 6 8 1 0 12 1 4 16 18 1Ü11 1 Ü 11

> w :L "--LJ 1 0 10 w (f)

"--N

* * 109

1 0 9

:L LJ "--z

z 1 0 8 10

8

X ::::l _J

LL 10

7 I 127( N2N 1I126 1 0 7

_J

0::

TI46tNPISC46 f-z 5321NPlP32

106

1 0 6 w FE541NPIMN54

O::'. NI581NPIC058 w LL U2381NFIF.P. LL NP2371NFlF.P.

0 1 0 5 1 0

5

0 2 4 6 8 10 1 2 1 4 1 6 1 8

ENERGY IN MEV


0. 5 - 1 .o Q.590 o.5 2.179E+10 1 . 0 - 1 . 5 0.923 1 .o 1 . 716E + 1 0 l . 5 - 2.0 1 . 023 1 . 5 l . 3 l OE+ 1 0 2. 0 - 3.0 1 . 013 2.0 9.849E+09 3. 0 - 4,5 o.955 3.0 5.301E+09 4. 5 - 6.0 1 . Of 5 4,5 1.94lE+09 6. 0 - 8.0 1 .133 6.0 6.673E+08 8.0 - 10.0 l .210 8.0 l .497E+08

lO.O - 14.0 o.744 lO.O 3.228E+07 l4.0-l8.0 l .023 l 4. 0 l.398E+06

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVITY DEVJATIONS

I1 1 2 1 3 !4 1 5 I 6 A1 A2 A3 R4

ORIGINAL 0.027 0. l 17 0°017 0.059 6. 60% 6. 46% 6.46%

FEW-GR. 0.023 0.099 0. 014 0.060

. MK. NH~~~~. JUGOSLRVJJR. SfT-3, C5-R.

FIG. 94

145

0 2 4 6 8 1 0 1 2 1 4 16 1 8 t o11 1011

> w :L "'--

1010 LJ 1010 w (f)

"'--N

* * 109

109

:L LJ "'--z

z 1 08

1 0 B

X :::J _J

LL 10

7 l 1271 N2N l l 126 107

_J

a:: Tl461NPl5C46

f--z 5321NPlP32

1 06

106 w FE541NPlMN54

n::: Nl581 NP lC058 w LL U2381NFJF ,p, LL NP2371NFJF.f.

D 1 0

5 10

5

0 2 4 6 8 10 1 2 1 4 16 1 8

ENERGY IN MEV


0. 5 - l .o 0.712 o.5 2°229E+l0 l. 0 - l. 5 0.961 l .o 1 .671E+10 1 . 5 - 2.0 0.945 1 ,5 l .248E+10 2. 0 - 3.0 0.952 2.0 9.472E+09 3. 0 - 4.5 0.943 3.0 5. l 95E+09 4. 5 - 6.0 l . 059 4 . 5 l 0 9l 4E+09 6. 0 - 8.0 1 . 107 6.0 6.476E+08 8.0-10.0 l . 145 8.0 l.418E+08

10.0-14.0 0.714 10.0 3.072E+07 14.o- 18.o 0.804 1 4 . 0 1 .099E+06

CHRRRCTERlSTIC INTEGRRLS RVERRGED RCTIVITY DEVIRTIONS

11 l 2 1 3 14 1 5 1 6 R1 R2 R3 R4

ORJGJNRL '.J. 016 0.067 0.012 0.036 6. 83% 7. 13% 7. l 3%

FEi'-GR. 0.013 0.049 0.009 0.034

. MR. NRJZER. JLJGOSLRVIJR. SET-3. CS-8

FIG. 95

146

0 ? 4 6 8 1 0 1 2 1 4 16 1 8 1 0 1.~1-r--+--t--t---l----J--t--+---+---+--+--4---4--4--..j..._-+--l---1-----<>- 1 0 11

> w :,;::: 'LJ w (f)

'N

* * :,;::: LJ 'z

z

X :::J _J

LL

_J

er:

~

z w n::: w LL LL

107

CU63[N2NlCU62

~--------------' Nl58(NPlC058 '------------_JFE54[NPlMN54 ~--------~ P31[NPlSl31

'-----------------' TH232lNFJf ,p, ~--------------' U238 ( NF l F. P.

'------------_J JNl 15[NNl!Nl 15M ~-----------'NP237[NFJF.P.

1 0 10

1127lN2Nl!12

D 10 5-+--l---+---+---+---+---+--+--+--r--1----1--+--+-~-+---l---l--4-"--+- 1 05

o 2 4 6 8 10 1 2 14 16 18

ENERGY 1 N MEV


0. 5 - 1 .o 0.782 o.5 2.339E+l0 1 . 0 - 1. 5 1 . 063 1 .o 1 .727E+l0 1 . 5 - 2.0 0.802 1 . 5 1 .259E+l0 2. 0 - 3.0 1 . 085 2.0 1 .004E+10 3. 0 - 4,5 0.896 3.0 5.163E+09 4. 5 - 6.0 1. 089 4,5 2.043E+09 6. 0 - 8.0 1 . 318 6.0 7.411E+08 8.0-10.0 1 . 143 8.0 1 .390E+08

10.0-14.o 0.634 10. 0 2.808E+07 14.0-18.0 1 . 289 l 4. 0 l . 762E +06

CHRRRCTERISTJC INTEGRALS RVERRGEO RCTIVITY OEVJATIONS

11 12 13 14 15 l 5

ORlGINRL 0.046 0.084 0.042 o.044 14.63% 8.02% 8.02% B .02%

FEW-GR. 0.034 o.033 0.035 o.024

. MR. NRJZER. JUG05LRVJJR. SET-4. CS-R

FIG. 96

> w l::

' u w (/)

' N

* * l:: u

' z

z

X ::::J _)

LL

_)

a: 1-z w ~ w LL LL

D

147

2 16 0 10 1~~-t-~t---ir---+~-+-~+-~t---+~-+-~-l-~+--+~-l-~-l-~4---+~-+~-t-10 11

18 4 6 8 10 12 1 4

10 1

1 0 9

10 8

~~~~~~~~~~~ FE54 ! NP l MN54 C S321NPlP32

~========~P3l!NPlSl31 '---------------' N 158 ! NP l C058

~=========:::=~ TH232 ! NF lF. P. '--------------' U2381 NF l F . P . L----------' lN115!NNl!Nll5M

.___ ________ _,NP237!NFlF.P.

1010

1 0 9

l 1271N2Nl1126 1 0 8

10 6

10 5-+-~+-~+----l~-+~-+-~+--~l----+~-l-~+-~+--4~-+~+-~+---1.....,;,.~~-1--10 5

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o 0.897 o.5 2.380E+l0 1 • 0 - 1. 5 1 . 122 1 .o 1 .ß78E+l0 1 • 5 - 2.0 o.694 1 . 5 1·184E+l0 2. 0 - 3.0 o.989 2.0 9.636E+09 3 .o - 4,5 0.936 3.0 5. l 95E+09 4 . 5 - 5.0 1 .058 4 . 5 1 °938E+09 6. 0 - 8.0 1 • 175 6.0 6.740E+08

8.0-10.0 1 .095 8.0 1 .371E+08

10.0-14.0 o.719 10. 0 3.085E+07 14.0-18.0 o.736 14. 0 1 . 006E +06

CHARACTERlSTlC INTEGRALS AVERAGED ACTlVITY DEVIATIONS

11 1 2 1 3 1 4 15 15

ORIGINAL 0.032 0°092 0.025 o.069 % 7.89% 7.89% 7.89%

FEW-GR. 0.016 0.018 0.o14 0.019

ifü. N~Jd:R. JJGIJSLHV!JR. SET-4. :::S-6

FIGo 97

148

0 2 4 6 8 1 0 12 1 4 16 18 1 0 9

10 9

> \ w :c ....... u w 1 08

10 8 <.f)

....... N

* * :c u

10 7 ....... 107 z

z

X 1 0 6

10 6 ::J _J 1127CN2Nlll26 LL AL27CNHElNA24 _J

CI S32CNPl Nl58CNPlC

f-1 0 5 1 0 5 z FE54CNPlMN

w TH232CNFlf .p, c::: U238CNFJf,p, w LL IN! 15( NN l !NI !SM LL NP2371NFJf,p,

D 1 o' 10 4

0 2 4 6 8 10 1 2 14 16 18

ENERGY IN MEV


0. 5 - 1 .o 0.958 o.s 2.645E+08 1 .o - 1 ,5 0.975 1 .o 1 .441E+08 1 . 5 - 2.0 0.880 1 ,5 8.688E+07 2. 0 - 3,0 1 '132 2.0 6.0l9E+07 3 '0 - 4,5 0.848 3.0 2.487E+07 4 '5 - 6°0 1 '2E.1 4,5 9.581E+06 6 .o - 8.o 1. 4 78 6.0 2.716E+(l6 8.0-10.0 0.900 8.o 4.953E+05

io.o- 14.o 0.713 10 .o 1 . 358E+05 14 .o - 18.0 0.636 14. 0 7.676E+03

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVJTY OEVJATIONS

11 1 2 1 3 1, 15 16 A1 A2 A3 A,

ORIGINAL o.086 0.033 o.070 0.032 14.59% 7 .77% 7 .77%

FEW-GR. 0.057 0.003 0.053 0.003

MR. NRJZER. JUCOSLnVIJR. ~[T-1 CS-R

F ~ G, 98

> w L: ....... (_)

w (/)

....... N )!( )!(

L: (_)

....... z

z

_J

cr

fz w Q::'.

w LL LL

0

149

0 2 4 6 8 16 18 10 9·---r~-r-~t-=-+~-+-~+--+~-+~4--~e---1-~-1-~1---1-~-1-~1--....+~-1--~.i-.10 9

10 12 1 4

10 8 10 8

10 6

.__ ________ __,TH232(Nflf,p,

'------------' U238( NF lf ,p. .___ _______ __, INl 15( NN l INl lSM

'----------' NP237( NF lf ,p.

10 4-+-~-1-~+--......,~--+~-1-~-1-~1--......+~--1-~-1-~+----+~.....i.:::....;;.-1-~+----1~......i.~-1-10 4

0 2 4 6 8 10 12 14 16 18

ENERGY 1 N MEV

ENERGY GROUP FLUX/REF. FLUX ,ENERGY INTEGRAL FLUX

0 ,5 - 1 .o 1 .027 0.5 2.683E+08 1 .o - 1 ,5 Q.987 1 .o 1 .391E+OB 1 .s - 2.0 Q.765 1 ,5 8.124E+07 2 .o - 3.0 1 . 047 2.0 5.803E+07 3 .o - 4.5 Q.892 3.0 2.538E+07 4 .s - 6.0 1 .234 4,5 9.308E+06 6 .o - 8.0 1 . 408 6.Q 2.589E+06 8.0-10.0 Q.850 e.o 4.737E+05

10.0-14.0 Q.703 10.0 1 .342E+05 14.0-18.0 0 .647 14. 0 7.805E+03

CHARACTERISTJC INTEGRALS AVERAGEO ACT!VITY OEVIAT!ONS

[ 1 1 2 1 3 [ 4 [ 5 [ 6

ORIGINAL Q.074 Q.043 Q.060 Q.050 14. 23% 7.31% 7.31%

FEW-GR. Q.053 0.003 0.040 Q.004

MR. NRJZER, JUGOSLRV 1 JR. SET-1 , CS-B

FIG. 99

> w ~

' u w (f)

' N

* * ~ u

' z

z

X ::J _J

lL

_J

a:

1-z w O::'. w lL lL

0

150

2 6 0 10 9·-r~=i--~+---.i~..+~-i.-~-+.-~1----+~--1-~,.;....~1----+~,,_j...~.J.-~J-.-___.~--1-~-+---10 9

1 6 1 8 4 8 10 1 2 14

'-----------' l 127 ( N2N l l 126 ~--"""=---------~ RL27(NHE lNR24

'--------~--------' FE56 (NP l MN56

i::::::==========~~ll l 46 (NP l SC46 ~--------~ S32(NPlP32 '----------~ Nl58(NPlC058 ~----------~ FE54(NPlMN54

'---------~ TH2321 NF lF .P. ~-------~ U238(NFlf.P.

~--------' NP237( NF lF ,p.

10 4-1-~...;..~~~~~~~~..i.-~..._~*"-'~-l--~~--l~.....$~-4-~~~"-l-~~~-J,_~~~""'-

o 2 4 6 8 10 1 2 1 4 16 1 8

ENERGY 1 N MEV


0 ,5 - 1 .o 0.951 o.s 2.644E+08

1 .o - 1 ,5 0.979 1 .o 1.436E+08 1 .5 - 2.0 o.842 1 . 5 8.614E+07 2 .o - 3.0 1 . 121 2.0 6.061E+07 3. 0 - 4. 5 0.949 3.0 2.565E+07 4. 5 - 6.0 1 . 211 4,5 8.550E+Q6

6 .o - 8.0 0. 911 6.0 1 .954E+06

8.0-10.0 1 °089 8.0 5.848E+05

10.0-14.0 0.795 10 .o 1 . 4 97E +05

14.0- 18.0 0.541 14. 0 6.535E+03

CHRRRCTER!STIC INTEGRALS RVERRGEO RCTJV!TY OEVJRTJONS

r, 1 2 1 3 1 4 15 l s

10 4

ORIGINAL 0.024 0.042 0 .027 0.041 13. 18% 11 . 02% 11 . 02%

FEW-GR. 0.014 o.003 0.015 0.004

MR. NRJZER. JUGOSLRVJJR. SET-('. CS-R

FIG. 100

151

0 2 4 6 8 10 12 14 16 18 10 9·-;-~-r-~!--'--t-~--r-~t---t~-+~+---1~-+~-+-~l----+~-l-~1---+~-+~-l--10 9

> w l:: -....... u w (/)

-....... N )!(

)!(

l:: u -....... z

z

X :::J _J

LL

_J

CI

fz w 0::: w LL LL

'-----------' l 127! N2N l 1126 c:=s:::::========::J AL 2 7 ( NHE l NA2 4 .__ _____ __,., _____ ___, FE56 (NP l MN56

c::::::::::::::::::::::::::::::~~Tl46!NPlSC46 .__ _______ ___, S32!NPlP32 '-----------' Nl58! NP lC058

.__ _______ ___, TH232! NF lF ,p.

'---------~ U238[ NF lF ,p. '------------' NP237[ NF lF ,p.

D !0 4--+~-+-~+---+~-+~-+-~+-~+---+~-+-~-+-~+---+~-l->-=-"-l-~+---+~-+~-+- 10 4

o 2 4 6 8 10 12 1 4 1 6 18

ENERGY IN MEV


0 ,5 - 1 .o 1 . 032 0.5 2.643E+OB 1 .o - 1 ,5 0.929 1 .o 1 .345E+OB 1 ,5 - 2.0 Q.717 1 . 5 8.004E+07 2 .o - 3.0 1 .027 2.0 5.829E+07 3 .o - 4,5 1 .ooo 3.0 2.624E+07 4. 5 - 6.0 1 .177 4,5 8.230E+06 6 .o - 8.0 Q.840 6.0 1 . 823E +06 8.0-10.0 1 . 036 8.0 5°620E+05

10.0-14.0 o.788 10.0 1 .483E+05 14.0-18.0 Q.547 14. 0 6.605E+03

CHARACTERJST IC INTEGRALS AVERAGEO ACTlVITY OEVIATJONS

11 1 2 l 3 !4 l 5 16

DR l G l NAL 0.027 0.039 0.030 0.044 13.50% 10.25% 10.25%

FEW-GR. 0°015 Q.005 0.015 Q.006

MK. NHJZtR, JUGOSLRV!JR. SET-2 CS-B

FIG. 101

152

0 2 4 6 8 10 12 14 16 18 10 9·-r~'i---"IF----+~-;-~-1---t~-+-~+---1~-1-~+...~l--....j..~-l-~l----i.~-+-~+-10 9

> w L:

' u w (f)

' N lt( lt(

L: u

' z

z

X :::::> _)

LL

_)

a:

fz w 0::: w LL LL

10° 1 0 8

,___ _________ __, FE54 (NP l MN5 .__ ________ ___, N 158( NP l C058

'----------' U238! NF lF ,p. .__ _______ _, IN115!NNlIN115M

.__ _____ ___, NP237!NF lF ,p,

D 10 4-!-~-l-~+--.......j~-+~-+-~+-~l---+~-+-~+-~,__-+~~.......:>-!-~+-.......j~....+-~-+- 10 4

o 2 4 8 1 0 1 2 14 16 18

ENERGY IN MEV


0 ,5 - 1 .o 0.967 o.5 2.705E+08 1 • 0 - 1 ,5 1 .019 1 .o l.489E+08 1 • 5 - 2.0 0.916 1. 5 8°915E+07 2. 0 - 3,0 1 .065 2.0 6. l 35E+07 3 .o - 4,5 1 .122 3.0 2.812E+07 4. 5 - 6.0 1.o.1 4. 5 7 .911E+06 6. 0 - 8.0 1 .202 6.0 2.408E+06 9.0-10.0 1 .098 s.o 6.025E+05

10.0-14.0 0.879 10.0 1 .639E+05 14.0-18.0 0. 483 14. 0 5.828E+03


I 1 I 2 I 3 I 4 I s I s

ORIGINAL 0.026 0.034 0.027 o.033 14. 65% 15.05% 15.05%

FEW-GR. 0.014 0.001 0.014 0.001

MR. NqJZEk. JUGüSLAVIJA. Stl-3 C5-R

FIG. 102

> L.J.J :c

" u L.J.J (f)

" N

* * :c u

" z

z

X ::J _J

LL

_J

0:

1-z L.J.J 0::: L.J.J LL LL

0

153

2 4 6 8 1 0 1 2 1 4 1 6

'-------------' 1127 ( N2N 11126 ~-=-.----------- AL 27 ( NHE 1NA24

c__ ___ __, _____ ___, CU63 ( NHE l C060

~---s=======~~~:=:=:=~= FE56 (NP 1 MN56

'---------------' N 1 58 (NP l C058 '-----------~ U238( NF IF ,p.

'-------------' !Nl 15rNNl!Nl 15M '---------~ NP237( NF lF .P.

18

0 )Q 4-t-~.,._.~+--~~-+~~~+-~1----t~-t-~.,._.~i=-=-....-+~~--"-F-~+--~~-+~-+- 10 4

o 2 4 6 8 10 12 14 16 18

ENERGY 1 N MEV


0. 5 - 1 .o 1 .037 o.5 2.732E+08 1 .o - 1 ,5 1 .021 1 .o 1 .428E+08 1 ,5 - 2.0 Q.785 1 ,5 8.295E+07

2. 0 - 3.0 Q.986 2.0 5.913E•07

3. 0 - 4. 5 1 . 154 3.0 2.837E+07

4. 5 - 6.0 1 .006 4,5 7.580E•06

6. 0 - 8.0 1 .016 6.0 2 .10IE+06

e.0-10.0 1 .037 8.0 5.737E+05

10.0-14.0 Q.852 10 .o 1 .593E+05

14.0-18.0 Q.502 14. 0 6.055E+03


l 1 l 2 1 3 1 4 1 5 l s

ORIGINAL 0.022 0.046 0°028 Q.056 13.50% 13.72% 13.72%

FEW-GR. 0.007 0.003 Q.008 0.003

MR. ~RJZER. JUGOSLRVIJR. SfT-1 [S-R

FIG. 103

> w l:::

' u w (f)

' N )1(

)1(

l::: u

' z

z

X :::J .....)

lL

.....)

[[

1-z w Q::'. w lL lL

D

0

154

2 4 6 8 1 0 1 2 1 4 16

'-------------' 1127 C N2N l 1126 '------------' MG2 4 (NP l NR24

~§;;;::::=========-:-::: RL27 r NHE l NR24 '------',__.;:, _______ __, C U6 3 C NHE l C 060 .____ ____ _,.___,_ _____ ____, FE 56 C NP l MN56

'------------'>...-V T 146 C NP l SC 4 6

'------------------' FES 4 ( N N54 '----------------' N 158 C NP l COS

'------------' TH232 ( NF l F • P. ~-------~ U238C NF lF ,p.

'-------------' INl 15CNNllN115M '---------~ NP237CNF lF ,p,

18

10 4-+-~-+-~+-~+-~1--.......;~--1=~--+-~-+-~+-~+----+~-+~.....j.>-="-l-~+-~+-----llm-----!-

o

11

2 4

ENERGY GROUP

0. 5 - 1 . 0 1 • 0 - 1 .s 1 . 5 - 2. 0 2.0- 3.0 3.0- 4,5 4.5- 6.0 6.0- 8.0 8.0-10.0

10.0-14.0 14.0-18.0

6 8

FLUX/REF. FLUX

1 .028 o.985 o.7ss 1. 038 1 • 024

1 °059 1 .026 1 • 202 o.713 o.676

CHRRRCTERlSTlC INTEGRALS

10 12 1 4 16 18

ENERGY IN MEV

ENERGY lNTEGRRL FLUX

o.s 2.687E+08 l .o 1 .395E+08 l . 5 8. l 68E+07 2.0 5.876E+07 3.0 2.637E+07 4,5 7.926E+06 6.0 2°159E+06 8.0 6.166E+05

10 .o 1.363E+05 14. 0 8 ° l 55E+03

RVERRGEO RCTlVITY OEVJRTJONS

ORlGJNRL 0.045 0.043 o.046 o.os1

104

13.58% 13.58% 13.58% FEN-GR. 0.013 0.003 0.011 o.004

MR. NRJZER. JUGOSLRVIJR. S~T-4 r.s-R

FIG. 104

155

T o N AKAVJlJRA

KYOTO IBJIV3RSITY, JAPAN

L'IETHOD:

The orthonormal expansion method is used to determine the

neutron spectrum. The neutron flux ~(E) is expanded in the

following series of orthonormal functions ~k(E),

. 11

~ ( E) = W ( E) 2: Clfx fk ( E) 7

~=-i

(1)

where n is the number of detectors, W(E) the weighting function -

and ak the coefficients of the expansion. The activation rate

A1 is given as 11

A~ = ~ Cl-R Si-k ~::.1

si,f(: LEo W(E)~ (E) <St (E) olE 1. (2)

The sclution of ~q.(2) gives uniquely the values of ak in Eq. (1).

In the LYRA code, a maximum energy E0 is a variable and the error

of the obtained spectrum is estimated.

In the spectrum evaluation of Annex II, the weight function

was given by

wo::)= e-o.776E s~~ J2i=

and the Laguerre polynomials were used as ~k(E). For spectr~m I

of Annex II, E0 was selected as 18.1 MeV. For spectrum II, E0

was selected as 12.5 MeV. This value of E0 was determined in the

following way: at first, the orthonormal expansion was processed

for 18.1 MeV of E0 and as a result, the evaluated neutron flux ~(E)

became negative near 12-MeV neutron energy, then E0 was truncated

at 12.5 MeV.

156

SPECTRA PROCESSED: I. Spectrum ( 1 result ) II. Spectrum f 2 results )

I„1., With CX = 0„776 ( Fig 105. )

IJI„1„ With ()( = 0„77€i ( Fig. 106„ )

II„2„ With a best <X „ (x' = 1.476„ ( Fig. 107. )

REPRESENTATION MODE OF THE SPECTRA: Differential spectra with 0.1 MeV between the energy points.

ENERGY REGIONS 0„1 - 18„0 Mev for the I 0 Spectrum; 0 0 1 - 12„5 Mev for the II. spectra„

GUESS' SPECTRUM LIBRARY: No

REMARKS: For the I.1 and II~1. spectra the value of ()(.was fixed to 0,776. For the II.2. spectrum the best value of d-. has been chooseni, and the calculations were aecomplished using this value„

> w :L

" (_)

w (f)

" N

* * :L (_)

" z

z

X ::i _J

LL

_J C[

1-z w Q:'. w LL LL

0

157

2 4 6 8 1 0

'---------------' AL271 NP '------------' 5321 NP lP32 ~------------' FE541NPl11N54

.___ ________ __, P31 1NPlS1 31

~------------' Nl58! NP lC058 '---------------' TH2321 NF l F. P. ~----------' U2381 NF lF .P.

.__ _______ ___, !Nl 151 NN l !Nl 1511

~-------~ NP2371NFlf,p,

12 1 4 16 18

1010

10°

0 10 5'-t-~~~F-=--t-~"'"F'-~T----+~~~~~~-+~-r-~1----+~-+--~+--+~->1-~-1-10 5

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV

ENERGY GROUP FLUX/REF. FLUX ENERGY 1 NTEGRAL FLUX

0 ,5 - 1 .o 0.554 o.5 2.284E+10 1 .o - 1 ,5 1 • 032 1 .o 1 .771E+10 1 • 5 - 2.0 1. 139 1 ,5 1 • 317E + 10 2. 0 - 3,0 1 °058 2.0 9.549E+09 3. 0 - 4,5 0°905 3.0 4.795E+09 4 ,5 - 6.0 0°887 4,5 1 °643E+09 6 .o - 8.0 0.930 5.0 5.824E+08 8.0-10.0 1 • 221 8.0 1 .575E+08

10.0- 14.0 0.893 10 .o 3.903E+07 14.0-18.0 1 • 465 14 .o 2.003E+06


11 1 2 1 3 1 4 1 5 16

ORIGINAL 0.027 o.091 0.019 0.038 6°66% 5.28% 5.28%

FEfl-GR. 0.022 0 .072 0.015 0.038

MR. NAKAMURR, .JRPl=lN.

FIG. 105

158

0 2 4 6 8 10 12 14 16 18 10 9 10 9

> w I:

' u w 1 0 8 10 8 (f)

' N llE llE I: u

10 7 ' 107 z

z

>< 10 6 106 =>

_J AL27CNHElNA24 LL.. HG24CNPlNA24 _J FE56CNPlHN56 cc NPl 2

1-10 5

FE N z NI58CNPl 10 5

w TH232CNF)f ,p, 0::: U238CNFJf ,p, w LL.. IN115CNNllN115H LL.. NP237CNFJf ,p,

0 104 10 4

0 2 4 6 8 10 1 2 1 4 16 18

ENERGY IN MEV


0 ,5 - 1 .o Q.520 o.5 2·118E+08 1 .o - 1 ,5 0.009 1 .o 1 .464E+08 1. 5 - 2.0 1 .206 1 . 5 9.431E+07 2 .o - 3.0 1 .226 2.0 5.771E+07 3 .o - 4,5 o.834 3.0 1 .947E+07 4. 5 - 6.0 o.387 4. 5 4.440E+06 6. 0 - 8.0 0.930 6.0 2.331E+06 0.0-10.0 2 .173 8.o 9.329E+05

10.0- 14.0 o.361 10.0 6.493E+04 14.0-18.0 14. 0

CHARACTERISTlC INTEGRALS AVERAGEO ACTlVlTY OEVlATIONS

I 1 12 I 3 l 4 15 ls A1 A2 A3 A4

ORIGINAL 0.433 0.217 o.371 0 .137 26.38% 19. 21 % 19 .21 %

FEW-GR. 0.374 0 .181 0. 314 0 .135

MR. NRKRMU~R. JRPRN. SFECTRUM 1

FIG. 106

159

0 2 4 6 8 10 12 14 16 18 10 9·-r~-r-~r----+~-i-~+-........J.~-i-~-i.---i~--1-~4-~1----1.~-1-~J.---1.~~~.i-10 9

> w ~ ....... u w (/) ....... N

* * ~ u ....... z

z

X ::i _J

LL

_J

a:

1-z w e::: w LL LL

1 0 8

10 7

,...'.::::::':~;::::::=====~MG24 C NP lNA24 ....__ _ ____,.,,.__ _____ _, AL 27 C NHE l NA2 4

....__ ____ ____,,.._ __ ___, FES 6 C NP l MNS6

.__ ________ __,TH232CNFlF.P.

'---------' U238C NF lF .P. .____ ______ __, INl lSCNNl IN! !SM

'---------' NP237C NF lF .P.

D 10 4---l--~-l--~+-----4~-l-~-l=-~.j.--~i-----+~-1-~-1--~l--~~--4-~*-~+-----4~-l-~-l-- 1 0 4

o 2 4 6 8 1 0 12 14 1 6 1 8

ENERGY 1 N MEV


0 .s - 1 .o Q.903 o.s 2.689E+08 1 .o - 1 .s 1. J S9 1 .o 1 .SS3E+08 1 . s - 2.0 1 .218 1 .s 8.738E+07 2. 0 - 3.0 Q.978 2.0 S.04IE+07 3 .o - 4.S 0.734 3.0 1 .988E+07 4 .s - 6.0 Q.81S 4. s 6.6S7E+06 6 .o - 8.o 1 .200 6.0 2.219E+06 8.0-10.0 Q.882 8.o 4. ! S7E+OS

10.0-14.0 Q.346 10 .o 6.327E+04 14.0-18.0 0.080 14 .o 9.668E+02


I 1 12 I 3 l 4 I s I5

ORIGINAL Q.042 Q.033 Q.039 Q.033 20.41% 11 . 12% 11 . J 2%

FEW-GR. Q.032 Q.014 0.033 Q.017

MR. NRKRMURR, JRPRN. 5PECTRUM t.

FIG. 107

V. SANGIUST

CESNEF, MILANO, ITALY

ME'!HHODS: SPECTRA /19/

SAiill-II /17/.

160

SPECTRA PROCESSED: L Spectrum ( 2 results ) II. Spectrum ( 2 results )

I.1. SPECTRA code ( Fige 108 ). I.2 „ SAND-II code ( Fig„ 109 ) •

II.1. SPECTRA code ( Fige 110 ). IL2. SAlJD-II coda ( Fig„ 111 ) •

REPR8SENTATION MODE OF TEE RESUIJTS: '.)6-point differential spectrum

~lillRGY :J~GION: 0.1 - 14.5 MeV.

GUESS SPECTJUM LIBRARY: No.

RE~/;ARKS : No •

161

0 2 4 6 8 1 0 12 1 4 1 6 18 1 Ü II 1 Ü II

> w :L ....... u 1010 w (f)

....... N

* * 109

1 0 9 :L u ....... z

z 1 08

108

X :::::> _J

LL 10

1 M 1 0? _J A a: FE56!

Tl46!NPlSC46 1-z FE54CNPlMN54

1 06

106 w NI58!NPlC058

0::: TH232CNFJF.P. w LL U238(NFJf,p, LL IN115!NNIIN115M

0 10

5 l 0 5

0 2 4 6 8 l 0 12 l 4 16 18

ENERGY IN MEV


0 ,5 - 1 .o 0 ,572 o.5 2.t26E+l0 1 .o - 1 .5 o.960 1 .o 1 .678E+l0 1 ,5 - 2.0 1 °006 1 ,5 1·256E+10 2 .o - 3.0 0.954 2.0 9.352E+09 3. 0 - 4,5 Q.912 3.0 5.Q65E+09 4 ,5 - 6.0 1 .041 4,5 1. 889E+09 6 .o - 0.0 1 °124 6.0 6°445E+08 0.0-10.0 1 °079 0.0 1 °311E+08

10.0-14.0 0°624 10 .o 2.635E+07 14.0-10.0 0.343 14 .o 4.685E+05


I, I 2 1 3 1 4 15 I s A1 A2 A3 A4

ORIGINAL o.019 0. 127 0 .011 0.015 9.01% 4 .14% 4 .14%

FEW-GR. 0.016 0 .107 0.000 Q.018

MR. SRNGIUST.ITRLY. SPECTRR CODE.

FIG. 108

162

0 2 4 6 8 1 0 12 1 4 16 18

101 1 Ü II

> w :r:

' 101 u 1010

w (f)

' N ll(

ll( 1 0

9 10

9 :r: u

' z

z 1 0° 108

X :::::l _J

lL 10

7 1 0

7

_J

a: TI46(NPlSC46

1-z FE54(NPlMN54

1 06

1 06 w NI58(NPlC058

Q:'. TH232(NFlf .p, w lL U238(NFlf.P. lL INl 15( NNl INl 15M

D 10

5 10

5

0 2 4 6 8 1 0 12 14 16 18

ENERGY 1 N MEV


0 ,5 - 1 .o 0.686 o.5 2°242E+l0 l .o - l .5 0.994 l .o l 0705E+l0 1 . 5 - 2.0 l .007 l .5 1 .268E+IO 2 .o - 3.0 0.973 2.0 9.471E+09 3 .o - 4,5 0.927 3.0 5 ° lOIE+09 4 ,5 - 6.0 l .035 4,5 l 0 873E+09 6 .o - 8.o l .098 6.0 6.353E+08 8.0-10.0 l .098 8.0 l . 336E +08

10.0- 14.0 0.639 l 0 .o 2°700E+07 14.0- 18.0 0.358 14 .o 4.895E+05

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVlTY DEVlATlONS

11 12 13 I 4 I 5 I 6 A1 Az A3 A4

ORIGINAL 0.014 o.074 0.009 0.009 8.55% 4. 14% 4. 14%

FEW-GR. 0.010 0.058 0.006 0 .011

MR. 5RNGIU5T,ITRLY. SRNC-11 CODE

FIG. 109

163

0 2 4 6 8 1 0 12 14 16 18 10 9

10 9

> w :c

' u w 10 8

10 8 (/)

' N

* * :c u

107

10 7

' z

z

X 10 6

10 6 ::::l _J

LL HG24CNPlNA24 _J AL27CNHElNA24 cc FE56CNPlHN56

TJ46 NPl 46 f-

10 5 1 0 s z FE54CNPl w Nl58CNPlCO Q:'. TH232CNFlf,p, w LL U238CNF)f,p, LL IN115CNNlJN115H

D 1 0 4

1 0 4

0 2 4 6 8 1 0 1 2 1 4 1 6 18

ENERGY IN MEV


0 ,5 - 1 .o 1 .694 Q.5 3.546E+08 1 .o - 1 ,5 l .Q70 1 .o 1.417E+08 1. 5 - 2.0 Q.860 1 ,5 7.891E+07 2 .o - 3.0 Q.835 2.0 5.281E+07 3 .o - 4,5 Q.982 3,0 2.676E+07 4 ,5 - 6.0 1 °299 4,5 9.070E+06 6 .o - 8.o 1 .200 6.Q 1 .996E+06 8.0-10.0 Q.4}3 8.0 1 .934E+05

10.0-14.Q 0 .156 10 .o 2.859E+04 14.0-18.0 Q.051 14 .Q 6. J 26E+02

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVITY OEVIATJONS

11 I z I 3 I 4 I s 16 A1 Az A3 A4

ORIGINAL 0. 154 o.516 o.088 0.273 26.08% 13.78% 13.78%

FEW-GR. 0 .125 o.368 0°068 0.261

MR. SRNGIUST. ITRLY. 5PECTRR CODE

FIG. 110

164 ...

0 2 4 6 8 10 12 14 16 18 10 9·-;-,-;-=--11-----t-~-t-~+-~~--+-~+---1~~~4-~l---l-~-J-~+--~~~~-1-10 9

> w l:: ....... u w (f)

' N

* * l:: u ....... z

z

_J

a:

1-z w O:::'. w IJ_ IJ_

1 o'

1 0 5

c=~;;:::====::J MG2 4 C NP l NA2 4 ~~====~===-::-= AL27 C NHE l NA24 .__ _____ ____,.,..::..... _ __, FE56 C NP l HN56

C46 '-----------------' FE54 C NP l M 4

.__ ________ __, NI58CNPlC058 '------------' TH232CNF IF ,p, .__ _______ __, U238C NF lF ,p.

.__ _______ __, IN115CNNllN115H

10 7

0 \0 4-+~+-~+-~+-~1----1~-+~-+-~~~+-~+----1~~~-1-........;i....._~~~+----<i--......j- 10 4

o 2 4 6 8 10 1 2 14 16 18

ENERGY IN MEV

ENERGY GROUP FLUX/REF. FLU:'. ENERGY INTEGRAL FLUX

0. 5 - 1 .o 1 .520 o.5 3.379E+08 1 . 0 - 1 ,5 1 .024 1 .o 1 .468E+08 1 . 5 - 2.0 0.959 1 ,5 8.670E+07 2 .o - 3.0 0.914 2.0 5.761E+07 3 .o - 4,5 1 .072 3.0 2.9!0E+07 4. 5 - s.o 1 .368 4,5 9.778E+06 6 .o - 8.0 1 .323 6.0 2.332E+06 8.0-10.0 0.704 a.o 3.437E+05

10.0-14.0 0.337 10.0 6.231E+04 14.0-18.0 0. 141 14 .o 1 .707E+03


11 1 2 13 14 l 5 16

ORIGINAL o.093 0. 311 o.076 0 .149 1383.21 13.58% 13.58%

FEW-GR. Q.078 0.206 0.067 0 .138

MR. 5RNGIU5T.ITRLY. 5RNO-II CODE

FIG. 111

L.,. TlJRI, A. FISCHER

CRIP BUDAPEST, HUN"GARY

165

.NIETHOD: RFSP ( a version of SPECTRA ) /22/

SPECTRA PROCESSED: I. Spectrum ( 1 result, Fig. 112 and 113. )

II·. Spectrum ( 1 result, Fig. 1l4 and 1~5. )

REPRESENTATION MODE OF THE RESULTS: 50-point differential spectrum, the flux 0(u) = E0(E) varies linearly between the energy points.

ENERGY REGION: 10-7 - 18.0 MeV.

GlJESS SPECTRUM LIBRARY: No.

RETi!ARKS : No •

> w L: '-.. u w (f)

'-.. N

)1( )1(

L: u '-.. z

z

X ::i _J

LL

_J

a:

fz w 0:::: w LL LL

0

166

0 2 4 6 8 1 0 12 1 4

CU63!N2NlCU62 .____ _______ __,! MG24!NP lNA24

""""----------' AL27! NHE lNA24 '------"'<--------' FE56! NP lMN56

~-------___,,,, _ __, AL 27 C NP l MG27 lP32

~-----------'FE54! MN54 '------------' P31 C NP l S 1 31

.____ ________ ___, N 158 ( NP l C058

'---------------' U238!NFlF ,p, .____ _______ ___, IN115!NNl!Nl 15M

'--------------' NP237! NF lf ,p. .__ _______ ___, PU239( NF lF ,p.

~-------~ U235!NFlf,p, 10 6.-j::::::::::===:::::::::J CU63( NGlCU64

o-------~ NA23!NGlNA24 ~---' AU197! NGlAU198 ,__ _ ___, C059 ( NG l C060

1 6 1 8

10 5--+-~-+-~+---IF---+~-+-~-+-~+---+~--+~-+-~+-~l---+~-+-~-+-~+-~--.....i-

o 2 4

ENERGY GROUP

0. 5 - 1 .o 1 • 0 - 1 • 5 1 • 5 - 2. 0 2.0- 3,0 3.0- 4,5 4.5- 6.0 6.0- 8.0 0.0-10.0

10.0-14.0 14.0-18.0

6 8

FLUX/REF. FLUX

o.678 1 • 248 1 .153 o.967 o.814 0.949 1 .035 o.939 o.543 0.794

1 0 1 2

ENERGY

0.5 1 .o 1 ,5 2.0 3.0 4,5 6.0 s.o

10.0 14. 0

1 4 16 1 8

ENERGY IN MEV

INTEGRAL FLUX

2.337E+10 1. 806E+ 10 l 0257E+IO 8.898E+09 4.554E+09 1.721E+09 5.873E+OB 1·148E+08 2°363E+07 1 • 086E +06

CHRRACTERISTIC INTEGRAL5 AVERAGEO ACTIVITY DEVIATIONS

ORIGINAL 0.026 0.110 1 .06E+5 0.030 0.102 9.78E+4

1 0 10

105

12 .87% 12.48% 11 ,91 % 9.63% FEW-GR. 0.017 0.075 5.22E+4 0.022 0.074 2.43E+4

MR TLIR 1 RNO F 1 SCHFR

FIG. 112

1 o-10 10-9 10-8 1 0-1 1 o-6 10-5 1 o-4 1 o-3 1 0-2 1 0- 1 10° 10 1 102

10111 1 1 1 1 1 1 1 1 1 1 1 1

10 II ~

> w ::;:: '-u

10 1~ ,,--------- ~ \ ,,......_ d ~ +1010 w

())

'-N

* * ::;:: u

10 9+ 1 / \ +io 9 '-z ~

'"tj z H ....... CU631N2N!CU6~D Q

MG24CNPINA24 X 1 0 8 ro· .... ::J AL27CNHElNA24 .... .... _J FE56CNPJMN56

°' V.! LL AL27CNPIMG27 -1 _J S32CNPJP32 c::::::J a: FE54CNPJMN54 c::::J .......

10 7 P31CNPISI31 r:::::J ~ +101

1-Nl5BCNPJC058 z c::::J

w U23BCNFJF.P. c:::::::J n:::: IN115CNNllN115M c:::::::::::J w NP237CNFJF.P. c=:=::J LL LL PU239CNFlf.P. ....... 106 1 +10

5 U235CNFJF.P. 0 CU63CNGICU64

NA23CNGINA24 AU197CNGJAU!98

C059lNGJC060

105 1 !

1 1 1 1 1 1 1 1 1 1 1 1 1 10 5

1 o-10 10-9 10-6 10-7 1 o-6 1 o-5 1 o-4 10-3 10-2 10-1 10° 101 102

ENERGY IN MEV

MR TURI RNO FISCHER

> w L:

" (_)

w (f)

" N

* * L: LJ

" z

z

X ::::l .....J LL

.....J er:

1-z w et::: w LL LL

D

168

0 2 4 6 8 10 12 14 16 18 10 9-r=~-t--~t---+~-+-~+---1~...+-~-1-~~--i.~ ....... ~.J.---1~--1-~-1-~~--i.~~10 9

.____ _____ ____, MG24C NP lNA24 '-----------' AL27C NHE lNA24

'---------->«,.------' S 32 C NP l P 32 .____ _____ __,...,,.._ __ __, FE54 C NP l MN54 .____ ______ ____,,_..._. NJ58C NP lC058

.__ ________ _,..,_r .____ _______ __, U238

'----------~ IN115CNNll .____ ____ __, NP237C NF lF .p .

NA23CNGlNA24 CU63CNGlCU64

1 0 5'-t:::==::i U235 C NF l F. P. 1-----' PU239C NF lF ,p.

MN55CNGlMN56 C059CNGlC060 AU197CNGlAU198

32CNF)f ,p, ,p .

10 4-+~-+-~+-~F---+~--1-~-1-~+---IF----l=~-+-~-1-~~----~;:...;..~-1--~.+-~1----1-

0 2 4 6 8 1 0 12 1 4 16 18

ENERGY IN MEV


0. 5 - 1 .o 1 .020 o.5 2.878E+08 1 . 0 - 1 ,5 1 . 227 1 .o 1.596E+08 1. 5 - 2.0 1. 113 1 .5 8.762E+07 2 .o - 3,0 1 .030 2.0 5.386E+07 3 .o - 4,5 o.753 3.0 2 .173E+07 4. 5 - 6.0 0.993 4,5 8 .172E+06 6 .o - 9.0 1. 483 6.0 2.765E+06 9.0-10.0 1 .14 7 8.0 5.366E+05

10.0-14.0 o.3'34 10 .o 7.854E+04 14.0-18.0 o.640 14 .o 7.728E+03

CHARACTERJSTJC lNTEGRRLS AVERAGEO ACTJVJTY DEVJATlONS

11 1 2 1 3 1 4 15 15 A1 A2 A3 A4

10 5

10 4

ORIGINRL 0.092 0.032 40.384 o.084 0.035 33.668 23.09% 16.79% 19.22% 4.89%

FEW-GR, 0.057 0.010 9.087 o.061 0.012 5 .191

MR -:-UR l RNO F 1 srnrn

FIG. 114

1 o-10 i o-9 i o-8 i 0-1 i o-s i 0-5 i o-4 i 0-3 i 0-2 1 0-1 1 0° 10 1 1 0 2

1012 1012 ~

> w ::;::: '-

1011+- /\ +1011 u

w (f)

'-N

* * 10 14 ~~ ~\ 0-- +1010 ::;::: u '-z -

~ z 10 9+ / 1 \ / \~ +109

H 0 .

X MG24C~4 D

t108

....... ::::i

..... _,. _J AL27CNHEJ 24 CJ °' 'J"' \.0 LL 108 S32CNPJP32 ~

_J FES4CNPJMNS4 a: NI58CNPJC058 ~ TH232CNFJf.P. f- U238CNFJf.P. z w 107 !Nll5CNNJIN!!SM ~ +10

1

a::: NP237CNFJf .P. w LL NA23CNGJNA24 LL CU63CNGJCU64 ~ U23SCNFJf.P. 0 10 6 ~ +10

5 PU239CNFJf.P.

MNS5CNGlMN56 COS9CNGJC060

AU!97CNGJAUl98

105

1 1 1 1 1 1 1 1 1 1 1 ' 1 10 5

1 o-10 10-9 10-8 10-7 1 o-s 1 o-5 10-4 1 0-3 1 0-2 10-1 10° 101 102

ENERGY IN MEV

MR TURI RND FISCHER

170

SKODA WORKS, CZECHOSLOVAKIA

METHOD: 1 0 RDMM/5/2. COCKROACH-code (an iteration effectivethreshold method after Bresesti )

SPECTRA PROCESSED: I. Spectrum ( 6 results ) II. Spectrunn: no.

I. 1 RDMM method, 8 detectors, the order of the polynom

is 7; ( Fig. 11:6 ) r.2 0 RDMM method, 6 detectors, the polynom order is 5;(Fig. 117}

I„3 RDMM method, 6 deteotors, polynom order is 6. ( F ig 11 8 ) I.4. COCKROACH method witfu 4 detectors; ( Fig. 119 )

I.5. COCICROACH method wita 5 detevtora; ~ Fig. 120) I 0 6 0 COCKROACH method with 6 detectors. ( Fig. 1e1 )

REPRESENTATION MODE OF THE RESULTS: Differential spectras

For the RDMM-resultd 31 - 31 points, for the COCKROACH-re-sults 4, 5 and 6 points respectively.

ENERGY REGION: RDMM: 0.4 - 14.0 MeV COCKROACH : 0.8 - 7.0 MeV

GUESS SPECTRUM LIBRARY: No.

REMARKS: The II. Spectrum could not be processed The detectov sev used by the authors did not permit to evaluate this spectrum succeafully ne~ther with the RDMM-code nor with the COCKROACH code 0

171

0 2 4 6 8 1 0 12 14 16 18 10 1 1011

> w l:: .......

1010 1010 u w (/)

....... N

llE

* 1 0 9 10 9 l:: u ....... z

z 1 08 1 0 8

X :::i _J

LL. 10 7 1 0? _J

CI

f-z

10 6 1 0 6 w AL271NPlHG27 O:::'. Nl581NPlC058 w LL. FE54!NPlHN54 LL. 1N1151NNl1N115H

0 1 05 10 5

0 2 4 6 8 1 0 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o 1 .686 0.5 3.274E+IO 1 . 0 - 1 ,5 1 .876 1 .o 1 .953E+IO 1 . 5 - 2.0 1 . 347 1 ,5 1. J28E•IO 2 .o - 3,0 o.730 2.0 6.994E+09 3 .o - 4,5 0 ,572 3,0 3.716E+09 4 ,5 - 6.Q o.936 4,5 1 . 723E +09 6 .o - 8.0 1 .073 6.o 6.050E+08 8.0-10.0 o.854 a.o 1.147E+08

10.0- 14.0 o.639 10 .o 3. l 83E+07 14.0-18.0 3,901 14 .o 5.333E+06

CHRRACTERISTIC INTEGRALS RVERAGEO ACTIVITY OEVIATIONS

1, 12 13 I 4 15 16 Al A2 A3 A4

ORIGINAL 0. 133 0.446 o.oat o.424 % 23. 4 6% 26.58% 26.58%

FEW-GR. 0 .114 0. 4 40 0.071 o.390

Skoda Works CZfCHOSLOVRK 1 R. ~~t!MM METHOO. SPECTRUM 1.

FIG. 116

172

0 2 4 6 8 10 12 1 4 1 6 18 10 1 j Ü 11

> w :r:

' 10 1 u 1 0 10

w (/)

' N

* * 10 9 1 0 9

:r: u

' z

z 10 6 1 0 6

>< :::l _J

LL 10 7 1 0 7

_J

a:

1-z

10 6 1 0 6 w 0:::: AL27CNPlMG27 w Nl58CNPlC058 LL LL INl 15C NN l IN115M

0 10 5 10 5

0 2 4 6 8 10 12 1 4 16 1 8

ENERGY IN MEV


0 ,5 - 1 .o 2.559 o.5 3.823E+IO 1 .o - 1 ,5 1 ,575 1 .o 1 . 819E + 10 1. 5 - 2.0 0.959 1 ,5 1 .082E+IO 2 .o - 3,0 o.708 2.0 7.767E+09 3. 0 - 4,5 0.022 3.0 4.585E+09 4 ,5 - s.o o.989 4 ,5 J.725E+09 6 .o - a.o o.911 s.o 5.429E+08 a.o - 10.0 o.903 a.o 1 .269E+08

10.0-14.0 0.841 10 .o 3.929E+07 14.0-18.0 3.230 14 .o 4.417E+06

CHARACTERISTIC INTEGRALS AVERAGEO ACTIVITY DEVIATlONS

11 12 1 3 14 15 16 A1 A2 A3 A4

ORIGINAL 0. J 74 1 ,554 0.000 1 .097 20.78% 26.60% 26°60%

FEW-GR. 0. J 70 1 .506 o.093 1 .226

Skoda Works . UECHOSLOVRK 1 R •• RDMM • SPECTRUM 2.

FIG. 117

173

0 2 4 6 8 1 0 1 2 l 4 16 18 10 1 l 011

> w l: ....... 1010 u 10 10 w (/) ....... N

* * 1 0 9 1 0 g l: u ........ z

z 10 6 1 ÜB

X ::J _J

lJ.. 10 7 10 7

_J

a: 1-z

1 0 6 10 6 w 0:::: AL27!NPll1G27 w lJ.. NI58!NPlC058 lJ.. IN115!NNlIN11511

D 105 10 5

0 2 4 6 8 1 0 1 2 14 1 6 18

ENERGY IN MEV


0. 5 - 1 .o 2.767 o.5 4.00IE+lO 1. 0 - 1 ,5 1 .683 1 .o J .834E+10 1 ,5 - 2.0 0.897 1 .5 1.094E+10 2 .o - 3.0 0.678 2.0 8.082E+09 3 .o - 4,5 0.953 3.0 5.037E+09 4 ,5 - 6.0 0.992 4 ,5 1.721E+09 6 .o - 8.0 0.891 6.0 5.352E+08 8.0 - 10.0 0.908 8.o 1 .284E+08

10.0-14.0 0.868 10.0 4.029E+07 14.0-18.0 3 °123 14 .o 4.270E+06


1, 12 I 3 14 15 1 s A1 A2 A3 A4

ORIGINAL 0.212 2 .127 0 °105 1. 437 19.00/. 24. 51 {. 24. 51 {.

FEW-GR. o.205 1 . 912 0 .111 1 .607

Skoda Works ' CZECHOSLOVRK 1 R •• RDMM ' SPECTRUM 3.

FIG. 118

174

0 2 4 6 8 1 0 12 1 4 1 6 1 8

101 J Ü II

> w ::E -......

101 1010 u

w (f)

-...... N

)IE )IE J,O 9 10

9

::E u -...... z

z 1 08 1 ÜB

X :::i _J

l.J... 1 0

7 10

7

_J

a: 1-z

106 10

6 w AL27CNHElNA24 0::: fE56CNPlMN56 w l.J... TH232CNFlf,p, l.J... NP237CNFJf,p,

0 1 05 10

5

0 2 4 6 8 10 12 1 4 1 6 18

ENERGY IN MEV


0 ,5 - 1 .o 1 .259 o.5 2.806E+10 1 .o - 1 ,5 1 .290 1 .o 1 .820E+10 1 ,5 - 2.0 1 .033 1 ,5 1 .253E+10 2 .o - 3.0 0.886 2.0 9.237E+09 3 .o - 4,5 Q.834 3.0 5.257E+09 4 ,5 - 6.0 0.955 4 ,5 2.353E+09 6 .o - 8.o 1 .001 6.0 1 .211E+09 8.0-10.0 1 .906 8.o 7.541E+08

10.0-14.0 7. 433 10.0 5.692E+08 14 .o - 18.0 190.690 14 .o 2.607E+08

CHARACTERISTIC INTEGRALS AVERAGEO ACTlVITY OEVlATIONS

1, l 2 l 3 I 4 I 5 l 5 A1 A2 A3 A4

ORIGINAL o.360 o.067 0.213 o.079 1149.96 167.09 167.09

FEW-GR. 0 .187 0.057 0 .131 Q.058

Skoda Works CZECHOSLOVRK i A. LÜCKt<UHCH. tiJ-'tC 1 RUM 1 •

FIG. 119

175

0 2 4 6 8 1 0 12 14 16 1 8 10 1 1 0 II

> w :E .......

10 1 10 10 u w (/) ....... N

* * 10 9 1 0 9

:E u ....... :z

:z 10 8 10 8

X :::J _J

LL 10 7 10 7

_J

a:

1-:z AL27CNHElNA24

1 0 6 10 6 w FE56CNPlMN56 Cl::'. i'.lL27CNPlMG27 w LL TH232CNFJf,p, LL NP237CNFlf ,p,

D 10 6 10 5

0 2 4 6 8 10 12 1 4 16 18

ENERGY IN MEV


0. 5 - 1 .o 1 .292 Q.5 2.750E+10 1 .o - 1 ,5 1 .287 1 .o 1.746E+10 1 . 5 - 2.0 1 ,QQ5 1 ,5 1 .1BDE+10 2 .o - 3.0 Q.867 2.0 B.59BE+09 3 .Q - 4,5 Q.828 3.0 4.705E+09 4. 5 - 6.0 Q.956 4 .5 1.B21E+09 6 .o - s.o 1 .001 6.0 6.787E+OB B.0-10.0 1 .286 s.o 2.216E+OB

10.0-14.0 1 .859 10.0 9.676E+07 14.Q-18.Q 14.362 14 .o 1.964E+07

CHARACTERISTIC INTEGRALS AVERAGEO ACTJVITY OEVIATIONS

11 12 13 14 15 16 A1 A2 A3 A4

ORIGINAL Q.041 Q.074 Q.041 Q.086 79.05% 22.04% 22.04%

FEW-GR. Q.033 Q.064 Q.029 Q.Q64

Skoda Works CZECHOSLOVRKJR. COCKRORCH. SPECTRUM 2.

FIG. 120

176

0 2 4 6 8 1 0 12 1 4 1 6 18 10 1 1 0 II

> w l:'.

' u w 10 1 1 0 10

(/)

' N

* * 10 9 1 0 9

l: u

' z

z 1 08 1 ÜB

X ::::::> _J

LL 10 7 1 0 7

_J

a:: AL27CNHElNA24

f-z FE56CNPlMN56

1 06 1 0 6 w AL27CNPlMG27 0::: FE54CNPlMN54 w LL TH232CNFlf ,p, LL NP237CNFlf ,p,

0 10 5 1 0 5

0 2 4 6 8 10 12 14 1 6 18

ENERGY 1 N MEV


0 ,5 - 1 .o 1 .102 o.5 2.737E+10 1 .o - 1 ,5 1 .361 1 .o 1 °874E+10 1 ,5 - 2.0 1 .275 1 ,5 1 .276E+10 2 .o - 3,0 0.864 2.0 8°697E+09 3 .o - 4,5 0.842 3,0 4.817E+09 4 ,5 - s.o 1 .023 4,5 1 . 885E +09 6 .o - s.o 0 ,95·5 s.o 6.630E+OB B.0-10.0 1 .286 8.0 2.216E+OB

10.0-14.0 1 ,959 10.0 9°676E+07 14.0-10.0 14.362 14. 0 1 . 964E +07


1, 12 I3 I 4 I 5 l s A1 A2 A3 A4

ORIGINAL 0.049 o.055 0.046 0.066 77.34% 17.43% 17.43%

FEW-GR. 0.035 0.040 0.032 0.047

Skoda Works LttCHOSLOVRK 1 R. COCKRORCH. SPECTRUM 3.

FIG • 121

177

W„L„ ZIJP

RCN PET'.l'EN, NETHEJ.LANDS

~.IETHODS: SPECTRA /19/, SAND-Ir /17/ „

SPECTRA ?ROCESSED: I„ Spectrum ( 2 resuits ) II. Spectrum ( 2 results )

I.1. SPECTRA code ( Fig. 122 and 123„ ). I.2„ SAND-II code ( Fig. 124 and 125. ). II.1. SPECTRA code ( Fig. 126 and 127. )e

II.2„ SAND-II code ( Fig„ 128 and 129„ )„

REPRESEl~TATION MODE OF THE RESULTS ~ 620-group flux for the

SAND-II raethod, 50-point raifferential flux for the SP~CTRA method„

ElTERGY R5GION: 1 o-1 O - 18„0 MeV

GUESS SPECTRUM LIBRARY: Yes

REMARKS: No.

z

X

LL

CI

f-z w 0::: w LL LL

D

178

0 2 4 6 8 1 0 1 2 1 4 1 6 18 1 0 1._,_1 +--+--f---!---1---4--+--+--1---+-.....j....--1---<---l---1--+---l--ol---1- 1 0 11

1010

CU63!N2NlCU62

~----------' 1127[N2Nll126 ~----------' MG24!NPlNR24

~;:;:========:::::::i RL27!NHE lNR24 ~--~---------' FE56 (NP l MN56

~---------"-<------~ RL27( NP lMG27

~-------~ TH232lNFlf.f. ~-------~ U238( NF lF .p. ~-------' IN115lNNl!N115M

~------~ NP237[ NF lF .p. 1~----~ U235lNFlf.P.

1~----~ PU239l NF IF .P. r::==::J C059 [ NG 1 C060

1 0 6 CU63( NGICU64

r::==::J RU 197 [ NG l RU 198 ,~ __ ___, U238 ( NG l U239

1~---' NR23lNGlNR24

1010

10 5-4---+---l---l--+----l----l---+--+---l---l--"--__. _ _... _ _.__-1-_-1-__;:;,_..>.....~10 5

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0. 5 - 1 .o Q.987 0.5 2.440E+10

1 . 0 - 1 .5 0.816 1. 0 1 .666E+10

1 . 5 - 2.0 1 .016 1. 5 1 • 308E + 10

2. 0 - 3.0 1 .070 2.0 9.843E+09

3.0 4. 5 Q.957 3.0 5.035E+09

4. 5 - 6.0 0. 941 4.5 1 • 706E +09

6 .o - 8.0 Q.958 6.0 5 .811E+08

8.0-10.0 1 . 016 8.0 1.434E+08

10.0-14.0 1 .041 10.0 4.479E+07

14.0-18.0 1 .166 14. 0 1 .594E+06

CHRRRCTERJSTJC INTECRRLS RVERRGED RCTJVJTY OEV'.RTJONS

11 1 2 1 3 1 4 15 1 s

ORIGINAL 0 .011 0.021 0. 4 18 0.012 0.020 0 .138 4.06% 4 .10% 3.85% 3.62%

FEW-GR. 0.004 Q.007 Q.391 0. 004 0.004 0. 157

MR. ZIJP, NETHERLRNO. SPECTRRL CODE.

FIG. 122

0\ !:'-.....

> w :L

" u w (D

" N

* * :L u

" z

z

X =i _J

lL

_J

a:

1-z w et:: w lL lL

0

1 0-1 1 o-6 1 0 -5 1 0 -4 1 0 -3 1 0- 2 1 0° 1 0- 1 1 0 l 10-10 10-9 1011 1011

102 1 0 -a

1010

109

1 0 a

107

106

j

;; /

/

// /

MG241NPINR24 RL271NHEINR24

FE561NPIMN56 RL271NPJMG27

P3!1NPJSI31 Nl581NPIC058 S321NPIP32 FE541NPIMN54 c::==::::=J TH2321NFJF.P. c::=::=::J U2381NFJF.P. c::=::=::J

lN1151NNllN115M i=:::::::::::J NP2371NFJF.P.

U2351NFJF.P. PU2391NFJF.P.

C0591NGIC060 CU631NGICU64 RU1971NGIRU!98 U2381NGIU239 NR231NGINR24

1010

109

1 0 B

107

106

105

105

10-10 10-9 10-a 1 0-1 1 o-6 10-5 1 o-4 1 0-3 1 0-2 1 0- 1 10° 101 10

2

ENERGY IN MEV

MR. lIJP. NETHERLRNO. SPECTRRL CODE.

~ N

0 H r:=..

> w L: '-. LJ w (f)

'-. N

* * L: LJ '-. z

z

X :J _J

lL

_J

er:

1-z w O'.'. w lL lL

180

0 2 4 6 8 1 0

CU63(N2NlCU62

'------------' U238(NFlF .P. ~-------___J IN115rNNlIN115M

'-----------' NP237( NF lF .P. 1~--------_J PU239( NF l F. P. 1~-------___J U235 ( NF l F. P. ,____ ___ __, U238 ( NG l U239

1 0 6'-J=-----~ CU63( NGlCU64 ,__ ___ _J AU197( NGlAU198

1-------~ NA23( NGlNA24 ,___ _ __, C059 ( NG l C060

1 2 1 4 16 1 8

1 0 10

D 10 5'-+---+--+--ll---+--+---+--1----l--+--4--+--l---+---+---l--1---.:::i'---l-)0 5

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV


0 .s - 1 . 0 o.749 o.5 2.404E+10 1 .o - 1 .s 1 • 022 1 .o 1 • 818E + 1 0

1 . 5 - 2.0 1 .184 1 .5 1.368E+l0 2. 0 - 3.0 1 .018 2.0 9.915E+09

3. 0 - 4.5 o.987 3.0 5.340E+09

4.5 6.0 1 . 074 4.5 1 .904E+09

6. 0 - 8.0 1 . 045 6.0 6.208E+08

8.0-10.0 1. 011 8.0 1 .433E+08

10.0-14.0 1 .057 10 .o 4.527E+07

14.0-18.0 1 .043 14. 0 1.426E+06

CHARACTERJSTIC INTEGRALS AVERAGEO ACTJVITY OEVIATIONS

11 1 2 1 3 1 4 15 16

ORIGINAL 0.008 o.049 7.89E+3 0.014 0.053 1 .60E+5 7.00% 4 • 4 2% 7.35% 4. 61 %

FEW-GR. 0.006 0.040 9.97E+2 0.010 0.042 1 .52E+3

MR. ZIJP, NETHERLRND

FIG. 124

1 o-10 i o-s 10-8 10-7 1 o-s i o-s i o-4 i 0-3 1 0-2 10-1 1 Ü G 101 102

1011 1011 ~

> w ::;::

' u 10 1~ ~\ (V 1 A f':/ ~ +iolO w

(f)

' N

* * ::;:: u

lO'T ,/\f i 1 V \ +109

' z CU63lN2NI - 1127( N2N 1.

z MG24lNPJNR24 RL27lNHEINR24

..... X 108

/ ~V / FE56lNPIMN56 rl +i 0

6 U'

00 ::::i RL27lNPIMG27 N

..... _J S32lNPIP32 LL FE54lNPJMN54

~\ Lo. .

ö _J P3! l NP ISl31 H

a: NI58lNPIC058 "" ~

107 TH232l NF IF .P. f-

U23BlNFJF.P. z c::::J w IN!l5lNNllNll5M c=::=J Ct:'. NP237lNFJF.P. w LL PU2391NFJF.P. LL U2351NFJF.P. ~

106 1 +10

6 LJ2381NGIU239 0

CU63lNGICU64 RU1971NGIRU!9B

NR23lNGINR24 C059lNGJC060

105

105

1 o-10 1 0 -9 1 0 -a 1 0 -7 1 0 -s 1 0 -s 1 0 -4 1 0 -3 1 0 -2 1 0- 1 10° 101

102

ENERGY IN MEV

MR. ZIJP. NETHERLRND

> w :r:: '-. LJ w (f)

'-. N

* * :L: (_)

'-. z

z

X ::::> _J

LL

_J

er:

fz w Cl:::'. w LL LL

D

182

0 2 4 6 8 10 12 14 16 18 10 9·-r~-r~t--""'""'f~-t-~,.....""""""i~-+~-+-~+----+~-l-~-F-~~~~-1-~i-.--J.~...j.-10 9

1 0 8

'----------' 1127 ( N2N l 1 126 1 Q7 ...--------~ AL27(NHElNA24

'----------' MG24(NPlNA24 .___ _________ __. FE56(NPlMN56

:::=========t;;:::====::::; S 32 ( NP l P 32 ~----___,,_....,,. __ ___, FE54 (NP l MN54 '---------+---''<----' N 1 58 ( NP l C05B

10 6 TH2 ( f,p, ...._ ____ _, U238( NF F ,p.

.___ ____ __, IN115(NNl N115 '-------' NP237( NF lF ,p.

NA23(NGlNA24 CU63(NGlCU64

10 5 N55(NGlMN56

C059(NGlC060 U235(Nflf,p,

1--~ PU239( NF lF. P. AU197(NGlAU19B

10 4-+-~-1-~+..-..-i---....+~-+=~-+-~+-----1~--4-~..+-~+----i---0. ....... -..~.-.~+-----1~----10 4

0 2 4 6 8 10 12 14 16 18

ENERGY IN MEV

ENERGY GROUP FLUX/REF. FLUX

0 ,5 - 1 • 0 0.832 1 .o - 1 • 5 0.981 1 • 5 - 2.0 0.942 2 .o - 3.0 0.920 3 .o - 4,5 0.993 4 ,5 - 6.o 0.717 6 .o - s.o 0.451 0.0-10.0 1 .106

10.0-14.0 1 .136 14.0-18.0 0.492

CHRRACTER!STIC INTEGRALS

ENERGY

0.5 1.0 1 ,5 2.0 3,0 4,5 6.0 s.o

10.0 14.0

JNTEGRRL FLUX

2.425E+OB l.379E+OB B.037E+07 5 .1 BOE+07 2.312E+07 5.233E+06 1 .329E+06 6.522E+05 2.103E+05 5.93BE+03

AVERAGED RCTIVITY DEVIATIONS

ORIGINRL o.104 Q.039 2.63E+2 0.037 o.035 2.69E+2 9,51;: 14.)4% 12.70% s.02;:

FEW-GR, 0 .OB! 0 .022 1 .5!E+2 0 .039 0 .020 1 .27E+2

MR. rl~IP.NFTHFR'.~NO. SPECTRRL CODE

FIG. 126

1 o-10 10-9 10-8 10-7 10-6 1 o-s 1 o-4 10~3 10-2 10-1 10° 101 l 02

10 12 I 1 1 1 1 1 1 1 1 1 1 1 1 1012 -> w ::;::

' 10 14 /\ +io11 u w (,')

' N

* * 10 1~ /~ \ V ~ ~ +1010

::;:: {'.._

u

' z ~

V V +10

9 l<'< z 109

c--00 ~ 0 N ..,._ D

X ::::) 0 _J

-t-1 0 8 ö

lL 106 H S32lNPlP32

""' _J FE54CNPlNN54 er: NI58CNPlC058 ~ TH232!NFJF.P. 1-z U238CNFJF.P. w l 0 7 lN115CNNllN!J5N c::::::\ +10

1

0::: NP237CNFJF.P. w lL NA23!NGlNA24 lL CU63CNGlCU64 ~ NN55!NGlNN56 0 1 0 6 \\ +10

5 C059CNGlC060

U235CNFJF.P. PU239CNFJF.P.

AU197!NGlAUJ98

105

1 1 1 1 1 1 1 1 1 1 1 . ) l 10

5

1 o-10 10-9 1 o-e 1 0-1 1 o-s 1 o-s 1 o-4 1 0-3 10-2 1 0-1 10° 101 102

ENERGY IN MEV

MR. lIJP.NETHERLRND. SPECTRRL CODE

> lJ.J :c ....... u lJ.J (/) ....... N

ME ME :c u ....... z

z

X =i _J

LL

_J

cr:

fz w a:: lJ.J LL LL

D

184 ...

0 2 4 6 8 10 12 14 16 18 10 9·-w-~+-~1---1=~-+-~+---+~-1-~-i-.--1~-+-~.+-........ 1---&.~-J.-~J--.....J.~...J-~.j._10 9

10 7 1127CN2N l 1126 '---------------' AL27C NHE lNA24 ~------------' HG24 (NP l NA24

C~~~~~~~~~~~~~~~:====::=i FE56C NP lHN56 S32CNPlP32 Nl58CNPlC058

c:::======+~=::::J Ff 54 C NP l HN54 1 0 6 T 2 NF l F • P •

'----------' U23 C NF • P. ..._ ______ _, IN! 15( N 1

'----------' NP237C NF lf ,p. CU63CNGlCU64

NA23CNGlNA24 10 6 N55CNGlHN56

C059CNGlC060 .__ __ __, PU239CNF lf ,p. 1-----' U235C NF lf ,p.

AUl97CNGlAUl98

10•-+-~+----l~-+~+-~+---+~-+-~+--4~-+~+----li---+.......::il>l-~+---+~-+----1-

0 2 4

ENERGY GROUP

. 0 ,5 - l. 0 l .o - 1 ,5 l ,5 - 2 .o 2.0 - 3.0 3,0- 4,5 4,5- 5.0 6.o- 9.0 9.0-10.0

10.0-14.0 14.0-18.0

6 8

FLUX/REF. FLUX

1 .106 1 .117 l .135 l .057 0.997 0.951 o.646 1 .o5r l .033 l .044

10 12

ENERGY

o.5 1 .o 1 ,5 2.0 3.0 4,5 6.0 9.0

10.0 14 .o

1 4 1 6 18

ENERGY IN MEV

INTEGRAL FLUX

2.965E+08 1 .575E+08 9. ! 97E+07 5.753E+07 2.454E+07 6.765E+06 1 .589E+06 6. ! 78E+05 ! .985E+05 ! .260E+04


10 6

1 0.

ORIGINAL 0.068 0.025 8°00E+2 0.040 0.027 1°72E+3

FEW-GR. 0.030 0.012 3.85E+2 0°019 0.012 4.04E+2 12.92% 1l.47% 9.81% 7.58%

. MR. ZIJP, NETHERLRNO

FIG. 128

1 o-10 i o-9 10-8 10-7 i o-s i o-5 i o-4 10-3 10-2 i 0- 1 10° 10 1 102

1012 i 1 1 1 1 1 1 1 1 1 1 1 1

1012 ~

> w ::L '-._

10 1-4- /\ 1 1\.' +ioll u 1 w (f) '-._

N llE llE 1 0 1.Q.f- /~ \~Ir' IJ ~F l1/l (\.._ +io

10 ::L u '-._

z -

V -1-10 9 ~ z 1 0 9 H 0

~ 0

X Cl

::J Cl N _J c::::::J

+108

~

'° LL 106 00 C::J V1

_J FE54CNPIMN54 a: NI58CNPlC058 ~ TH232CNFlf.P. t--

U238CNFJF.P. z w 10 7 lN115CNNlIN1ISM c:=:::::\i +10

1

a::: NP237CNFlF.P. w LL CU63CNGlCU64 LL NA23CNGlNA24 ~ MN55CNGlMN56 D 10 6

C059CNGlC060 \\ +106

PU239CNFJF.P. U235CNFJF.P.

AU197CNGlAU!98

10

5

' 1 1 1 1 1 1 1 1 1 1 ' 1 10

5

1 o-10 10-9 10-8 10-7 10-6 10-5 10-4 1 o-3 10-2 10-1 10° 101 102

ENERGY IN MEV

MR. llJP. NETHERLRND

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