Backscatter neutron spectrometer

W. Udo Schröder, 2011

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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

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Neutron Cross Sections

1b=10-24cm2

=100fm2

n-hydrogen n-carbon

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r, 20

11

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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.

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Associated-Particle/Neutron TOF

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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

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Applications

W. Udo Schröder, 2011

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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

qq

q

+=

+ + > 0

forward scattering

vn

W. Udo Schröder, 2011

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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

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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

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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

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MANDI-01

A Mobile Accelerator-Based Neutron Diagnostic Imager

W. Udo Schröder, 2011

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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.

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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

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