1. Interactions of Neutrons
with Matter

2. Commercial Neutron Generator ING-03
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
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
Rad Inter Neutrons
Alternative option: T(d,n)4He, En15 MeV
Source: All-Russian Research Institute of Automatics VNIIA
W. Udo Schröder, 2003

3. Nuclear Interactions of Neutrons
No electric charge  no direct atomic ionization  only collisions and reactions with nuclei  10-6 x weaker absorption than charged particles
Processes depend on available n energy En:
En ~ 1/40 eV (= kBT) Slow diffusion, capture by nuclei
En < MeV Elastic scattering, capture, nucl. excitation
En > MeV Elastic+inel. scattering, various nuclear reactions, secondary charged reaction products
Characteristic secondary nuclear radiation/products:
g-rays (n, g)
charged particles (n,p), (n, a),…
neutrons (n,n’), (n,2n’),…
fission fragments (n,f)
Rad Inter Neutrons
W. Udo Schröder, 2003

4. Neutron Cross Sections
1b=10-24cm2=100fm2
Rad Inter Neutrons
W. Udo Schröder, 2003

5. Mean Free Path of Neutrons in Water
Neutron Mean Free Path 35 30 25 20 15 10 5
Neutron Energy (MeV)
Neutron Mean Free Path (cm)
Mean Free Path of Neutrons in Water
r: atomic density s: cross section
l = average path length in medium between 2 collisions
Rad Inter Neutrons
W. Udo Schröder, 2003

6. Neutron Resonance Capture
n-107Ag  108Ag*
Quantal resonance effect at low and thermal n energies  wave nature of neutrons
Rad Inter Neutrons
W. Udo Schröder, 2003

7. Energy Transfer in Elastic Scattering
qlab
Neutron with lab velocity , energy E, scatters randomly off target nucleus of mass number A at rest in lab.
n A
c.m.
vn vA
qlab
vcm|Lab vn
vn|Lab q
lab velocity of center of gravity
Rad Inter Neutrons
W. Udo Schröder, 2003

8. Neutron Energy Spectrum
Neutron with energy E0 scatters off target nucleus A at rest in lab.
Lab energy spectrum (1 coll.) En
dP/dEn-A
qlab
vcm|Lab vn
vn|Lab q
q = 180o
q = 0o
The laboratory energy spectrum of scattered n reflects the center-of-mass scattering angular distribution !
Rad Inter Neutrons
W. Udo Schröder, 2003

9. Multiple n-A ScatteringEi
P(En-A)
N = 2
N =3
<E1>
<E2>
<E3>
Incoming n energy E0 = < E0>, N successive scattering events
“Logarithmic Decrement” x
Rad Inter Neutrons
W. Udo Schröder, 2003

10. Thermalization Through Scattering
N-therm: E0=2 MeV  0.025eV A x
N-therm 1
1.0000 18 12
0.1578
115 65
0.0305
597
238
0.0084
2172
Rad Inter Neutrons
W. Udo Schröder, 2003

11. n Angular Distribution
qlab
vcm|Lab vn
vn|Lab q vn
Rad Inter Neutrons
> 0  forward scattering
W. Udo Schröder, 2003

12. A Dependence of Angular Distribution
Properties of n scattering depends on the sample mass number A
 Measure time-correlated flux of transmitted or reflected neutrons
Light Nucleus
qlab
Heavy Nucleus
qlab
Rad Inter Neutrons
Light nuclei: slowing-down and diffusion of neutron flux
Heavy nuclei: neutrons lose less energy, high reflection/transmission
W. Udo Schröder, 2003

13. Principle of Fast-Neutron Imaging (2)
neutrons neutrons
sample
f(0)  d  f(d)
incoming transmitted
Rad Inter Neutrons
Transmission decreases exponentially (reflectivity increases) with thickness and density of sample, for most materials.
W. Udo Schröder, 2003

14. Number of collisions E0  E1
Neutron Diffusion
Multiple scattering = statistical process
Heavy materials (A>>1): random scattering
Number of collisions E0  E1
Probability for no collision along path length x: P(x)
for l = const.
Rad Inter Neutrons
W. Udo Schröder, 2003

15. Mean Free Path of Neutrons in Water
Neutron Mean Free Path 35 30 25 20 15 10 5
Neutron Energy (MeV)
Neutron Mean Free Path (cm)
Mean Free Path of Neutrons in Water
r: atomic density s: cross section
l = average path length in medium between 2 collisions
Rad Inter Neutrons
W. Udo Schröder, 2003

16. n-Stopping and Scintillation ProcessGd g e-
delayed
delayed light
Organic Scintillator Liquid
Diffusion Regime e- e-
Prompt Injection of mn neutrons
10-8s
10-7s
10-6s
10-5s
10-4s
Rad Inter Neutrons
diffusion mn interactions
time
time=0
W. Udo Schröder, 2003

17. A Mobile Accelerator-Based Neutron Diagnostic Imager
MANDI-01
Rad Inter Neutrons
W. Udo Schröder, 2003

18. Principle of Fast-Neutron Imaging (3)
time
intensity
primary neutrons
secondary radiation
Neutron interactions with sample nuclei may produce characteristic secondary radiation:
g-rays (n, g)
charged particles (n, a),…
neutrons (n,n’)
fission fragments (n,f)
depending on the sample material
Secondary radiation induced by neutrons in the sample appear with the same frequency as the neutron pulses.
Rad Inter Neutrons
Detectors for characteristic secondary radiation improve recognition of sample material, reduce ambiguities.
W. Udo Schröder, 2003

19. Design and construct MANDI test mounts & hardware
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
Stage I
Rad Inter Neutrons
Stage II
W. Udo Schröder, 2003