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Backscatter neutron spectrometer
W. Udo Schröder, 2011
Rad
In
ter
Neu
tron
s 2
Nuclear Interactions of Neutrons
Characteristic secondary nuclear radiation/products:
1. g-rays (n, g)2.charged particles (n,p), (n, a),…3.neutrons (n,n’), (n,2n’),…4.fission fragments (n,f)
No electric charge no direct atomic ionization Magnetic moment interaction with magnetized materials Collisions and reactions with nuclei 10-6 x weaker absorption than for charged particlesProcesses depend on available n energy En:En ~ 1/40 eV (= kBT) Slow diffusion, capture by nuclei
En < 10 MeV Elastic scattering, capture, nucl. excitation
En > 10 MeV Elastic+inel. scattering, various nuclear reactions, secondary charged
reaction products
W. Udo Schröder, 2011
Rad
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Neu
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s 3
Neutron Cross Sections
1b=10-24cm2
=100fm2
n-hydrogen n-carbon
Rad
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Neu
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sW
. Udo
Sch
röde
r, 20
11
4
Neutron Mean Free Path
xs
x
x
FWHM x
Pass x without collision
P x N x N e
Gaussian Prob.Distribution
Range Straggling
x xdN xdx
x
mfp
2
2
2 2
:
( ) 0
( )
( )exp
2
; 2
2.35
1 1( )
Mean Free Path of Neutrons in Water
r: number density (atoms/ volume), s: cross section
l = average path length in medium between 2 collisions
Los Alamos nuclear data files
W. Udo Schröder, 2011
Rad
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Neu
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s 5
Neutron DiffusionIn very thick absorbers, e.g., water tanks, concrete walls:Multiple scattering = statistical processHeavy materials (A>>1): random scattering
00 0
. ., :
1.... ; . lnN
NN
But E const const N collisions
EE E E e logarithmic decrem
N Ex
l
x-
¹ ® ¹æ ö÷ç ÷® ® » = ç ÷ç ÷çè ø
2 2 2 2
0 02
x x
N
Mean square displacement along trajectory
x N dxx e dxel l
l l¥ ¥- -
-
= = =ò ò
Probability for no collision along path length x: Ps(x)Probability for collisions at [x, x+dx]: dPcoll=-dN/N(x)=-1/l
for l = const.( )( )( )
( ) 1x
collcolls
d N N xdP xdP x e dx
dx dxl l
-= ® = =
W. Udo Schröder, 2011
Rad
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s 6
Energy Transfer in Elastic Scattering
|
. . : 0
11 11
1
n A n A
n A
cmLab
cm p p p p
Av v v v
A A
v vA
= - + =
= = -+ +
=+
|
|
max :
1min :
1
nLab
nLab
v v
Av v
A
=
-=
+
Neutron with lab velocity , energy E, scatters randomly off target nucleus of mass number A at rest in lab.
qlab
qlab
vcm|Lab
vnvn|Lab
vn
vn
q
( )( )
|2
| 2
| |
max :
1mi
max,
n
n
:
mi :
1
n La
n
n Lab cmLab n
Lab
bE
v
E
v
E
v
AE
A
-=
=
+
±
=
n A
c.m.
vn vA
lab velocity of center of gravity
v
W. Udo Schröder, 2011
Rad
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s 7
Scattered-Neutron Energy Spectrum
( )
( )
( ) ( ) ( )
| | | |
|
22 2 2
|
2 2 2
2
| | |
| |
| |
2
2 cos1
sin .sin
n Lab cmLab cmLab cmLab
cmLab
n Lab
n Lab n Lab n Lab
n A n Lab n A n Labn A
n Lab n Lab
E v v v v v v v
Av v v
A
dE dE dEconst
d d d
d E dP Ed
d dE dE
q
qq q q
ss q - --
µ = + = + + ×
= + ++
µ ® µ =W
Þ µ µW
r r r r r r
r r
2
0 0
11
AE E
A
æ ö- ÷ç ÷ç ÷çè ø+
Neutron with energy E0 scatters off target nucleus A at rest in lab.
qlab
vcm|Lab
vnvn|Lab
vn
vn
q
( )
2
02
11n
AE E
A+
=+
En
dP/d
En
Lab energy spectrum (1 coll.)
The laboratory energy spectrum of scattered n reflects the center-of-mass scattering
angular distribution !
q
=
0o
q
=
180
o
W. Udo Schröder, 2011
Rad
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s 8
Multiple n-A Scattering
( )
( )
1
11 0 0
22 1 0
1
2
0
2
1
0
.................
1
1)
1
1
(
NN N
E E E
E E E
E E E
P EE
A
A
a a
a a
a
a
-
é ùê úê ú= =ê úê úë û
=
+
=
= =
Þ =-
+
( ) ( )( ) ( )
( )
0
0
10 1 1
2 2
10 02
0ln1
: ln ln1 1
ln 1 11 1 ln ( )
2 (
ln
22 31)1
E
E
A
x x xE E dE P E dE E
A Af E
A A
E
E
A
aa
a a a
a
x
a a>
é ù-ê úë û= = = =- -
æ ö+ + ÷ç ÷= + = + ¾¾ ¾® ¹ç ÷ç ÷ç +-
æ ö÷ç ÷ç ÷ç ÷çè ø
+è ø
ò ò
Incoming neutron energy E0 N successive elastic scatterings
Evaluate “Logarithmic Decrement” x
0 0ln ln N
N NE E N E E e xx -» - ® » ×
N = 1
Ei
P(E
n-A) N =
2
N =3
<E1><E2><E3>
W. Udo Schröder, 2011
Rad
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Neu
tron
s 9
Thermalization Through Scattering
0ln ln
NE E Nx= -
0
0
( )
ln : ln ln
( )
N
N
Define E as median mean
E E E N
E N E e x
x
-
<
= = -
= ×
%
%
%
A x N-therm
1 1.0000 18
12 0.1578 115
65 0.0305 597
238 0.0084 2172
N-therm: E0=2 MeV 0.025eV
W. Udo Schröder, 2011
Rad
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Neu
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s 1
0
Slow-Neutron Resonance Capture
n-107Ag 108Ag*Quantal resonance effect at low and thermal n energies wave nature of neutrons
Excited Ag* nucleus deexcites and/or b-decays
W. Udo Schröder, 2011
Rad
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s 1
1
n-Stopping and Scintillation Process in Thick Detector
e- e-
10-7s
10-6s
10-5s
10-4s
10-8s
diffusion delayed@8MeV mn
interactions
GdGd
g
g g
g
g e-
e-
delayed
delayed light
Fast Moderation Process Organic Scintillator
Diffusion Regime
time
time=0
Gd
n1
n2
n3
Prompt Injection of m neutrons
ii
LOP
LOP
SuperBall Neutron Calorimeter
Rad
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W. Udo Schröder, 2011
13
Rad
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W. Udo Schröder, 2011
14
Pulse Shape Analysis
fast componentslow
I
t2t1t0
Particle 1
Particle 2
1
0
2
1
1
2
1 2
( )
( )
( )
t
t
t
t
Q I t dt
Q I t dt
Q Q Q L Energy
2 signals of equal total light output
Q1-Q
2Q
1-Q
2
Total n-H Cross Section Parameterization
Approximate parameterization for applications (detector efficiency estimates)
Cross section in barns (b)1b = 10-24cm2
22
2
3( )
1.206 1.86 0.0941 0.0001306
1.206 0.4223 0.13
n
bE
E E E
b
E E
Rad
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W. Udo Schröder, 2011
16
Non-Linear Light Output Response
1 2 3 20.18 5.25( )
0.63 1.10 5.25
p p
e p
p p
MeV E E MeVE E
E MeV E MeV
NE 213 liquid scintillator: e-equivalent energies Ee Ep
For a given energy, electrons & photons have the highest light output
Thin-Detector Light Output Response
Rad
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Neu
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s
W. Udo Schröder, 2011
17
Thin detector:1 n-p interaction within detector (n leaves)Equivalent to g-e Compton
Each fixed neutron energyproduces recoil proton energy (Ep) distribution produces distribution in LO(light output).
LO response is calibrated with g-rays electron-equivalent energy Eee (eVee).
Convert measured Eee Ep
Unfold Ep distribution
1 Light Output Response 5”x2” NE-213 1.5 2.0 Neutron Energy 2.1 2.5 3.0 MeV
Equivalent to full-energy peak? Thick detector (many l thick)
Rad
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W. Udo Schröder, 2011
18
Efficiency of p-Recoil NeutronDetectors
EndP/d
Ep
q
=
0o
Ep=E
n
ET
F1 F2
5”x2” NE-213
Electronic detector threshold
2
1 2
( , ),
( , )
( ) 1
( ) ( )
n T
Tn
n
n X n y nX y
FE E
F F
EE
E
E E all n induced
ET
angle dependent n-p energy transfer continuous recoil energy spectrum
Detector Efficiency Estimates
, , 1 1 exp ( )ThTh n H
EE E d E n d
E
Detector thickness d =10cmHydrogen density (atoms/cm3) NE-213nH=4.86·1022/cm3
Eth=1 MeV
Approximate intrinsic detection efficiency e(E)Probability for detection if incident neutron trajectory is perpendicular to detector face.
Total efficiency contains e(E) and solid-angle factor DW.
Rad
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s
W. Udo Schröder, 2011
19
Associated-Particle/Neutron TOF
Rad
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W. Udo Schröder, 2011
20
Reference time-zero t0: true TOF = tmeas-t0 a) from accelerator signal, b) associated particle* of known E c) g-ray* (v=c)*measured with same or different detector
d= target-detector flight distance
d
2
2
0
:
2 2
( )( )
Non relativistically
m m dE
t t
Spectrum
dN t EdN E dt
dE dt dE
tg
Rad
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s
W. Udo Schröder, 2011
21
Applications
W. Udo Schröder, 2011
Rad
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Neu
tron
s 2
2
n Angular Distribution
( )
|
2 2| |
22
2
( )
1 2 cos1
1 1n cmLab
n Lab n cmLab
v vv A v
v v v
v
A
A
A A
A
q
= =
= + =
é ù= + +ë û
+ +
+
r r r
1
21
1 coscos
1 2 cos
1 2cos
2 3Lab dA A A
A q
qqq
+
-
+
+=
+= ò
( )22 2 2 2| | | |
2 2 2
2 cos |: 1
1 2 cos 1 2 1 2 cos cos
n n Lab cmLab n Lab cmLab Lab
Lab
v v v v v v A
A A A A A
q
q q q
= + - +
é ù= + + + - + +ë û
qlab
vcm|Lab
vnvn|Lab
vn
q
2
1 coscos
1 2 cosLab
A
A A
q
+=
+ + > 0
forward scattering
vn
W. Udo Schröder, 2011
Rad
In
ter
Neu
tron
s 2
3
A Dependence of Angular Distribution
1
0
cos 2/ (3 )
22 3
2( ) exp
( 2 3)
( )
lab
lab
Average scattering
A A
AN
E N EA
After N collisions
q
pq
-= µ
-
ì üï ï-ï ïï ï» × í ýï ï+ï ïï ïî þ
R
:
%
Properties of n scattering depends on the sample mass number A
Measure time-correlated flux of transmitted or reflected neutrons
qlab
qlab
Light Nucleus
Heavy Nucleus
Light nuclei: slowing-down and diffusion of neutron flux
Heavy nuclei: neutrons lose less energy, high reflection & transmission
W. Udo Schröder, 2011
Rad
In
ter
Neu
tron
s 2
4
Principle of Fast-Neutron Radiography(Imaging)
( ) (0) ( )
( )
.A A
T
T e Transmission
N
atten coeff
material density
d
f d f d
d
m r s r
m
r
- S×
= ×
=
S = × = × ×
=
=
(0) f d f(d )
incoming transmitted
neutrons neutrons
Transmission decreases exponentially (reflectivity increases) with thickness and density of sample.Neutrons more penetrating use for thick samples
sam
pl
e
Comparison of different radiations
W. Udo Schröder, 2011
Rad
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Neu
tron
s 2
5
Commercial Neutron Generator ING-03
Source: All-Russian Research Institute of Automatics VNIIA
1300 mm
rear connectors
source
window
Specs: < 3·1010 D(d,n)3He neutrons/s Total yield 2·1016 neutrons
Pulse frequency 1-100Hz Pulse width > 0.8 ms, Power 500 W Alternative option: T(d,n)4He, En14.5 MeV
Neutrons can be produced in a variety of reactions, e.g., in nuclear fission reactors or by the D(d,n)3He or T(d,n)4He reactions
W. Udo Schröder, 2011
Rad
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s 2
6
MANDI-01
A Mobile Accelerator-Based Neutron Diagnostic Imager
W. Udo Schröder, 2011
Rad
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Neu
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s 2
7
Neutron interactions with sample nuclei may produce characteristic secondary radiation: 1.g-rays (n, g)2.charged particles (n, a),…3.neutrons (n,n’)4.fission fragments (n,f)depending on the sample material
Principle of Fast-Neutron Imaging (3)
time
inte
nsi
ty
primary neutrons
secondary radiation
Secondary radiation induced by neutrons in the sample appear with the same frequency as the neutron pulses.
Detectors for characteristic secondary radiation improve recognition of sample material, reduce ambiguities.
W. Udo Schröder, 2011
Rad
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Neu
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s 2
8
Required R&D• Design and construct MANDI test mounts &
hardware• Measure n energy spectra and angular
distributions with and without different types of collimators.
• Design and test B-loaded plastic shielding/moderator.
• Perform extensive pulsed-beam coincidence measurements of 2.5-MeV n transport through a range of materials varying in density and spatial dimensions.
• Measure n amplification in thick fissile targets• Assess sensitivity and quality of transmission and
backscattering imaging • Develop computer model simulations• Develop large-area detectors (e.g., BF3 or BC454
B-loaded scintillation counters)• Develop and test dedicated electronics
Sta
ge I
Sta
ge II