WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx 1
Joint Research Centre (JRC)IRMM - Institute for Reference Materials and MeasurementsGeel - Belgiumhttp://irmm.jrc.ec.europa.eu/http://www.jrc.ec.europa.eu/
Covariance data of experimental
observables in the resonance region WONDER 2009
29 September – 2 October, 2009CEA, Cadarache
P. Schillebeeckx1), A. Borella1), S. Kopecky1), C. Lampoudis1), C. Massimi1,2), M. Moxon, N. Otsuka3), I. Sirakov1,4)
1) EC- JRC – IRMM, Geel Belgium2) INFN, Bologna, Italy3) IAEA – NDS, Vienna, Austria4) INRNE – Sofia, Bulgaria
2WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Problem
( σ, Vσ ) determined by :• Reaction model : σ = F(θ)
– R-Matrix; HF+WF; Optical Model
• Calculation Method for Vσ
– Simple model (transformation of variables): P(σ) dσ = Q(θ)dθ
– MC-simulations
– Vσ ≈ Gθ Vθ GθT with Gθ = δF/δθ
• Input parameters : (θ, Vθ)– (θ, Vθ) determined by adjustment to experiment (χ2- minimization)
Reaction Model(σ, Vσ) (θ, Vθ)
θ θ θθ ≈ μ + θ − μF( ) F( ) G ( )
3WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Reliable model parameters by adjustment to experiment
Requirements:
• Experimental observables and relations to model parameters are
defined
• All uncertainty components are identified, quantified and
documented (uncorrelated & correlated)
• Verify the impact of correlations due to calibration (normalization)
uncertainties on the minimization of χ2
4WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Experimental observables
Capture (fission) Transmission
Self-indication
tneT σ−≈ ...)e1(Yt
n t +σ
σ−≈ γσ−
γ
...))e1((e,Yt
nnSI tt1 +
σ
σ−≈γ γσ−σ−
n1 n
5WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
σ(n,γ) measurements 103Rh(n,γ)
104 105 106 107100
102
104
Bi AuNa
C'w
B'w
Res
pons
e / (
1/ns
)Time Of Flight / ns
104 105 106 10710-4
10-2
100
C'ϕ
B'ϕ
Res
pons
e / (
1/ns
)
Time Of Flight / ns
Flux measurement Capture measurement
''
'w
'w
rexp
BCBCNY
ϕϕ
ϕ
−
−ε
σ=
6WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
AGS: Data reduction + uncertainty propagation
C’ dead time corrected counts
B’ background contribution
N normalization factor''
'w
'w
rexp
BCBCNY
ϕϕ
ϕ
−
−ε
σ= '
out'out
'in
'in
expBCBCNT
−
−=
Reaction yield + Self-indication Transmission
Histogram operations + Covariance information (AGS)
Models
Yexp + covarianceYSI,exp + covarianceTexp + covariance
input
WONDER 2006
7WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
SZ : correlated partdim. (n x k)
DZ : uncorrelated partn values
Analysis of Geel Spectra (AGS)
• Transform count rate spectra into observables (transmission, yields + SI )
• Full uncertainty propagation starting from counting statistics
• Output: complete covariance matrix
• Special format for covariance matrix– Reduce space for data storage (EXFOR)– Document the sources of uncertainties due to
each step in the data reduction processX Z Dz Sz
Special format for full covariance information
Observable Z (dimension n) with k sources of correlated uncertainties
TZZZZ SSDC +=
8WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
10-1 100 10110-3
10-2
10-1
100
101
Cap
ture
Yie
ld
Energy [eV]
n + 197Au 0.5 mm ENDF/B-VII
197Au: σ(nth , γ) = (99.0 ± 1.0) b <--> (98.7 ± 0.1) b
4x100 5x100 6x100
10-1
100
Cap
ture
Yie
ld
Energy [eV]
n + 197Au 0.5 mm ENDF/B-VII
2x10-2 3x10-2 4x10-21.5x10-1
2.0x10-1
2.5x10-1
3.0x10-1
3.5x10-1
4.0x10-1
Cap
ture
Yie
ld
Energy [eV]
n + 197Au 0.5 mm ENDF/B-VII
Absolute determination of σ(n,γ)
9WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Correction for n- and γ-transportimplemented in REFIT
1 10 10010-3
10-2
10-1
100
Yexp YM, REFIT (+ att.) YM, REFIT (no att.)
Yie
ld
Neutron Energy / eV
4 5 60.0
0.5
1.0
Yie
ldNeutron Energy / eV
0 1 2 30.00
0.05
0.10
0.15
0.20
0.25
0.30
Yie
ld
Neutron Energy / eV
WF depending on σtot, WONDER 2006
Borella et al., NIMA 577 (2007) 626
10WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Resonance shape analysis
FM is a model describing the transmission observable TM, with model parameters:
RP resonance parameters σtot(RP)
Experimental parameters θ:R resolution TOF-spectrometer
TD Debye temperature (Doppler effect)
n number of atoms per unit area ⇒ Resonance parameters adjustable parameters
)TT(V)TT()RP( Mexp1,T
TMexp
2 −−=χ −θ10000 20000 30000 40000 50000
-4
4
Res
idua
ls
Neutron Energy / eV
0.2
0.4
0.6
0.8
1.0
Tran
smis
sion
10000 20000 30000 40000 50000
-404
Sputtering target n = 1.92 10-2
Res
iuda
ls
0.2
0.4
0.6
0.8
1.0
Tran
msm
issi
on
Mn powder n = 9.94 10-3
Time-of-flight11
,TT
RP )DVD(V −θ
−θθ=
,...)R,n,T,RP(FT DMM =
11WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
nΓ<<Γγ nΓ>>Γγ
Γ
ΓΓ∝ γ
γn
JngA ngn ΓγΓgn• Capture(weak resonances)
ngn Γ γΓΓngn
thin,tA ngn Γ• Transmission ngn Γ
For (Γ >> ΔD and ΔR) ⇒ Γ = Γn + Γγ directly from observed shape
• Self-indication(thick – thin)
Resonance parameters: (ER, Γn, Γγ , J(π), l )
n1,SI gn
AΓ
Γ∝γ
γΓΓ∝ nthick,t gnA
gn11 n1 gn Γ
Γγ
)1I2(21J2g
++
=
l from transmission
Fröhner, ND1966, p. 55
12WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Spin of 4.9 eV resonance for 197Au + n
4 5 6
0
Res
.
0.0
0.5
1.0
J = 2
Tran
smis
sion
4 5 6
0Res
.Neutron Energy / eV
0.0
0.5
1.0J = 2
Tran
smis
sion
4 5 6
0
Res
.
Neutron Energy / eV
0.0
0.5
1.0
J = 1
Tran
smis
sion
4 5 6
0 Res
.
0.0
0.5
1.0
J = 1
Tran
smis
sion Only gΓn
Γn can be wrong by 40%
Uncertainty on Γn ?
83g =
85g =
Simultaneous RSA using REFIT
13WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Spin of 4.9 eV resonance for 197Au + n
J = 1 J = 2
Simultaneous RSA using REFIT
14WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
0.0
0.2
0.4
0.6
0.8
1.0
Texp TM,REFIT
Tran
smis
sion
Dependence of VRP on measurement type4.9 eV resonance for 197Au+n
4.0 4.5 5.0 5.5 6.00.0
0.2
0.4
0.6
0.8
1.0
Texp TM,REFIT
Tran
smis
sion
Neutron Energy / eV
10 μm
50 μm
Γn = ( 15.06 ± 0.08) meV
Γγ = (121.7 ± 1.3 ) meV
ρ(Γn, Γγ) = 0.55
⇒
⇒
Γn = ( 14.66 ± 0.30) meV
Γγ = (124.8 ± 3.7 ) meV
ρ(Γn, Γγ) = - 0.96
VT,exp: only uncorrelated uncertainties due to counting statistics
ΔD ∼ 80 meV
L = 50 m ΔR ∼ 5 meV
15WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
4.0 4.5 5.0 5.510-3
10-2
10-1
100
Yexp YM,REFIT
Yie
ld
Neutron Energy / eV
10-3
10-2
10-1
100
Yexp YM,REFIT
Yie
ld
L = 30 m5 µm
L = 12 m5 µm
Γn = ( 15.31 ± 0.12) meV
Γγ = (118.0 ± 1.4 ) meV
ρ(Γn, Γγ) = - 0.50
⇒
⇒
Γn = ( 15.26 ± 0.15) meV
Γγ = (118.9 ± 1.2 ) meV
ρ(Γn, Γγ) = - 0.63
VY,exp: only uncorrelated uncertainties due to counting statistics
ΔD ∼ 80 meV
ΔR ∼ 8 meV
ΔR ∼ 20 meV
Dependence of VRP on measurement type4.9 eV resonance for 197Au+n
16WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Id-number Measurement Distance Angle
(flight path – moderator)
Target thickness
T1 Transmission 50 m 9o 10 μm
T2 Transmission 50 m 9o 50 μm
C1 Capture 30 m 0o 5 μm
C2 Capture 12 m 18o 5 μm
Measurements Γn / meV Γγ / meV ρ( Γn, Γγ )
VZ,exp: only uncorrelated uncertainties due to counting statistics
T1 15.06 ± 0.08 121.7 ± 1.3 0.55
T2 14.66 ± 0.30 124.8 ± 3.7 - 0.96
C1 15.31 ± 0.12 118.0 ± 1.4 - 0.50
C2 15.26 ± 0.15 118.9 ± 1.2 - 0.63
T1 + C1 15.14 ± 0.07 120.0 ± 1.0 0.06
T1 + C2 15.10 ± 0.07 120.2 ± 0.9 - 0.29
T1 + T2 + C1 + C2 15.14 ± 0.06 119.8 ± 0.7 - 0.47
Dependence of VRP on measurement type4.9 eV resonance for 197Au+n
17WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Resonance parameters for natCd
Kopecky et al., NIMB 267 (2009) 2345 - 2350
Experiment ⇒ Data reduction with AGS ⇒ Resonance Shape Analysis
Thin – Thick transmission(1.3610-4 2.2410-4 at/b)
l = 0 J =1 χ2 = 0.98l = 0 J =0 χ2 = 1.30
0.1 0.2 0.3 0.4 0.5
-3
0
3
Res
idua
ls
Neutron Energy / eV
0.3
0.6
0.9
exp. data REFIT
Tran
smis
sion
Parameter p / meV ρ(pi,pj)
ΔD ∼ 20 meVΔR ∼ 0.2 meV ( L = 50 m)
ER 178.7 ± 0.1 1.00 0.53 0.28
Γγ 113.5 ± 0.2 1.00 0.26
Γn 0.640 ± 0.004 1.00
18WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
113Cd : impact of uncertainty components(only transmission)
Data reduction: dead time and background
Data reduction: uncorrelated uncertainties (counting statistics)
Parameter p / meV ρ(pi,pj)
ER 178.7 ± 0.068 1.00 0.43 0.79
Γγ 113.5 ± 0.15 1.00 0.43
Γn 0.640 ± 0.0007 1.00
Parameter p / meV ρ(pi,pj)
ER 178.7 ± 0.069 1.00 0.43 0.64
Γγ 113.5 ± 0.16 1.00 0.31
Γn 0.640 ± 0.0011 1.00
19WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Data reduction: counting statistics, dead time, background
Parameter δpini p δp ρ(pi,pj)
ER Γγ Γn L n TD N
ER / meV - 178.7 ± 0.074 1.00 0.53 0.28 0.13 0.00 0.00 -0.34
Γγ / meV - 113.5 ± 0.22 1.00 0.26 0.20 0.02 -0.04 -0.70
Γn / meV - 0.640 ± 0.0036 1.00 0.11 -0.91 -0.00 -0.28
L / m 0.006 26.4439 ± 0.006 1.00 -0.00 0.01 -0.09
n / (at/b) 0.5 % ± 0.5 % 1.00 0.00 -0.00
TD / meV 0.5 % 25.46 ± 0.5 % 1.00 0.00
N (norm) 0.5 % 1.000 ± 0.0013 1.00
Parameter p / meV ρ(pi,pj)
ER 178.7 ± 0.069 1.00 0.43 0.64
Γγ 113.5 ± 0.16 1.00 0.31
Γn 0.640 ± 0.0011 1.00
113Cd : impact of uncertainty components(only transmission)
20WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
GELINA (transmission + capture) + ORELA (transmission) RETROSPECTIVE Borella et al. PRC 76 (2007) 014605 and Horen et al. PRC 20 (1979) 478 Rochman and Koning
NIM A589 (2008) 85
ER gΓn / eV gΓγ / eV gΓnΓγ/(Γn+ Γγ) / eV ρ(Γn, Γγ) ρ(Γn, Γγ)
3.36 0.570 ± 0.004 0.146 ± 0.001 0.116 ± 0.001 - 0.15 - 0.16
66.00 82.210 ± 0.414 1.398 ± 0.018 1.375 ± 0.017 0.03 - 0.00
92.61 32.0 1.503 ± 0.017 1.436 ± 0.016
92.61 32.0 ± 16.0 ? 1.503 ± 0.017 1.436 ± 0.016 - 0.77
92.61 32.0 ± 4.0 1.503 ± 0.017 1.436 ± 0.016 - 0.10
Vθ from uncertainties in literature(retrospective ?)
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
Γ∂∂Γ∂
∂
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
σσ
σσ
⎥⎥⎦
⎤
⎢⎢⎣
⎡
Γ∂∂
Γ∂∂
=σ
γΓΓΓ
ΓΓΓ
γγγ
γ
K
K
)
)KK n2
,(
,(2
nK
n
nn
γ
γ
Γ+Γ
ΓΓ=
n
ngK
206Pb + n
21WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
1 10 100 1000100
101
102
103
104
5.19 eV18.83132.002850102710
C'ϕ
B'ϕ
Black Resonances
TOF
- spe
ctru
m /
(1/n
s)
Time-Of-Flight / μs
1 10 100100
101
102
103
B'γ
B'γ1
C'γ
B'γ
B'γ0
B'γ1
C'γ
B'γ =aoB'
γ0 + a1B'γ1
Time-Of-Flight / μs
B'γ0ϕϕ
γγϕγ
−
−
ε
σ=
BC
BCNY
'
'
rexp,
Borella et al., NSE 152 (2006) 1-14Borella et al., NIMA 577 (2007) 626
B’ϕ = b0 + b1 TOFb2
20 22 24 10000 10000010-4
10-3
10-2
10-1
100
Normalization URR
232Th(n,γ)t = 0.5 mm
Y
exp
Neutron Energy / eV
Internal normalization+ WF depending on σtot
Uncertainty 1.5%
232Th(n,γ) in URR
22WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Borella et al. NSE 152 (2006) 1-14
Emin Emax σγ δσγ δσγ,u ρ
keV keV mb (%) (%)
4 6 1107.9 0.49 0.17 1.00 0.60 0.57 0.58 0.55 0.53 0.62 0.58 0.56 0.61 0.58 0.54 0.51
6 8 934.2 0.44 0.19 1.00 0.55 0.56 0.53 0.51 0.60 0.57 0.55 0.60 0.56 0.53 0.49
8 10 845.1 0.43 0.21 1.00 0.54 0.51 0.49 0.58 0.55 0.52 0.57 0.54 0.51 0.47
10 15 749.1 0.38 0.15 1.00 0.52 0.50 0.59 0.56 0.54 0.59 0.55 0.52 0.49
15 20 638.7 0.39 0.18 1.00 0.48 0.57 0.54 0.52 0.56 0.53 0.50 0.47
20 30 571.3 0.36 0.14 1.00 0.55 0.52 0.50 0.54 0.51 0.48 0.45
30 40 490.3 0.32 0.18 1.00 0.61 0.59 0.64 0.61 0.57 0.54
40 50 429.6 0.31 0.19 1.00 0.56 0.61 0.58 0.54 0.51
50 60 382.9 0.33 0.22 1.00 0.59 0.56 0.52 0.49
60 80 311.4 0.30 0.18 1.00 0.61 0.57 0.54
80 100 242.5 0.33 0.22 1.00 0.54 0.51
100 120 217.8 0.33 0.23 1.00 0.48
120 140 201.6 0.33 0.24 1.00
232Th(n,γ) in URR Uncertainty propagation AGS
Correlated: uncertainty dead time, background (capture)
23WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Emin Emax σγ δσγ δσγ,u ρ
keV keV mb (%) (%)
4 6 1107.9 1.70 0.17 1.00 0.85 0.85 0.86 0.86 0.87 0.88 0.88 0.88 0.89 0.89 0.88 0.88
6 8 934.2 1.64 0.19 1.00 0.88 0.89 0.89 0.89 0.91 0.91 0.91 0.92 0.92 0.91 0.91
8 10 845.1 1.63 0.21 1.00 0.89 0.89 0.90 0.91 0.91 0.91 0.92 0.92 0.91 0.91
10 15 749.1 1.61 0.15 1.00 0.90 0.91 0.93 0.92 0.93 0.93 0.93 0.93 0.92
15 20 638.7 1.61 0.18 1.00 0.91 0.92 0.92 0.93 0.93 0.93 0.93 0.92
20 30 571.3 1.59 0.14 1.00 0.93 0.93 0.93 0.94 0.93 0.93 0.93
30 40 490.3 1.56 0.18 1.00 0.95 0.95 0.96 0.95 0.95 0.95
40 50 429.6 1.56 0.19 1.00 0.95 0.96 0.95 0.95 0.95
50 60 382.9 1.55 0.22 1.00 0.96 0.96 0.95 0.95
60 80 311.4 1.55 0.18 1.00 0.96 0.96 0.96
80 100 242.5 1.56 0.22 1.00 0.96 0.95
100 120 217.8 1.55 0.23 1.00 0.95
120 140 201.6 1.55 0.24 1.00
Borella et al. NSE 152 (2006) 1-14
232Th(n,γ) in URRUncertainty propagation AGS
Correlated: uncertainty dead time, background,+ normalization (1.5%)
24WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
232Th in URR Parameterization in URR by HF + WF
0 50 100 150
10
15
20
25
CRP-evaluation Iwasaki et al. Poenitz et al. Uttley et al. Vertebnyj et al. Kobyashi et al. Gregoriev et al.
σ(n,
tot)
/ b
Neutron Energy / keV0 50 100 150
60
70
80
90
100
σ(n,
γ) E
1/2 /
(b
eV1/
2 )
CRP-evaluation Borella et al. Aerts et al. Kobayshi et al. Macklin et al.
Neutron Energy / keV
Sirakov et al., Annals of Nuclear Energy 35 (2008) 128
Code developed by I. Sirakov(IRMM - EFNUDAT project)
25WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Sensitivity to average parameters(included in output)
0 50 1000
20
40
60
80
100
Neutron Energy / keV
(<σ n,
γ > E
1/2 )
/ (b
arn
eV1/
2 )
σn,γ
s p d
0 50 10010-2
10-1
100
( δ<
σ n,γ>
/ <σ n,
γ >) /
(δθ
/ θ)
S0
S1
S2
Tγ,0
1/2+
Tγ,0
1/2-
Neutron Energy / keV
Capture cross section dominated by l = 1and mainly determined by Tγ
-1/2 + impact of S1
26WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
232Th(n,γ) : Covariance matrix in URR
<σγ>Uncorrelated 1.0 %Correlated 1.5 %
<σγ> + < σtot>1.0 % 0.5 %1.5 % 1.0 %
+ S0 with uS0 = 0.5%
θ (uθ /θ) x 100
ρ x100 (uθ /θ) x 100
ρ x100
S0 16.3 100 - 81 - 18 32 23 0.5 100 - 16 38 - 13 28
T0+1/2 5.9 100 - 17 19 - 54 3.0 100 - 23 74 - 43
S1 4.7 100 - 65 79 2.0 100 - 21 52
T1-1/2 3.7 100 - 74 2.7 100 - 80
S2 20.0 100 11.2 100
En / keV (uσγ /σγ)
x 100 ρ x100 (uσγ /σγ)
x 100 ρ x100
5 1.54 100 96 96 90 1.49 100 99 96 93
10 1.53 100 97 92 1.42 100 98 91
50 1.51 100 93 1.43 100 94
100 1.63 100 1.48 100
27WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Reliable model parameters from experiment
Requirements:
Well documented experimental observables in EXFOR
Including:
- experimental details ( RF, TD, n, …)
- all uncertainty components (correlated and uncorrelated)
⇒ Proposal IAEA / IRMM based on AGS
28WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Uncertainty in literature (Phys. Rev. C)
Results only based on capture cross section measurements
29WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
[1] NSE 160 (2008) 200 - 206[2] NIM A 179 (1981), 13[3] NIM A 228 (1985), 217[4] NIM A 531 (2004), 392
Main Reference 1
Template for resonance cross section datain EXFOR
Facility GELINA 2,3 Neutron production 4
Primary neutron production target Uranium Time resolution primary beam (ns) 4 ns Moderator material H2O Surface Dimensions (mm x mm or diameter in mm)
2 containers 100 x 100 mm
Thickness (mm) 40 mm Experimental details
Measurement type Fission Flight path length (m) (moderator – target (detector): face to face distance)
(8.218 +/- 0.006) m
Angle (with respect to normal of moderator)
18 deg
Beam dimensions (mm x mm or diameter in mm)
Diameter 55 mm
Sample Type (metal, powder) Electrodeposition Chemical composition UO2 Atomic abundance of main element 99.9732 at% 236U Weight per unit area (g/cm2) (209.9 +/- 1.3) Uμg/cm2 Geometry
Surface dimensions (mm x mm or diameter in mm)
Diameter (50.0 +/- 0.1) mm
Thickness of main element (at/b) 5.354 10-6 at/b 236U Backing 20 μm aluminium
Containment description No container Temperature 25 meV
Proposal IRMM & NDS - IAEA
30WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Template for resonance cross section data in EXFOR
AGSOutput
Detector Type Frisch gridded ionisation chamber Material CH4 (100%) Gas pressure Gas flow at 1 atm Geometry 2π
Flux normalization Reaction 10B(n,α) Cross section from ENDF/B-VI.8 Atomic abundance of main element 93.0 at% 10B Target thickness (8.05 +/- 0.10) 10B μg/cm2 Surface dimensions Diameter (50.0 +/- 0.1) mm
(236U- 10B : back to back) Normalization uncertainty (TOF-independent)
1.5 %
Data
Time-of-flight of first channel 3000 ns Time-of-fligth bin width / ns Column 1 Energy (relativistic formula, L = 8.238 m) eV Column 2 Yield in barn/at Column 3
Uncertainties (at 1 sigma level) Total (normalization not included) Column 4 Uncorrelated contribution (variance) Column 5 Other sources creating correlated uncertainty components
Dead time 10B [col 6] Background 10B [col.7, 8,9] Dead time 236U [col. 10] Background 236U [col.11,12,13]
31WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Time-of-flight <-----> Energy
n
'n t
Lv =
L’m
R(L’m)
Detector
L0
L’ = L0 + Lm
En
e- beam
Analytical expressions in REFIT include storage term of Ikeda & Carpenter
10-2 100 102 1040
2
4
6
8
<Lm>
/ cm
Ikeda and Carpenter (analytical) MCNP
Neutron Energy / eV
32WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx
Acknowledgementsupport through
• EFNUDAT– 197Au (C. Massimi)– Code for URR (HF + WF) (I. Sirakov)– REFIT : include new options (M. Moxon)
• NUDAME– Cadmium
• NDS – IAEA • JEFF project