Interaction of Neutrons 

with Matterwith Matter

2/4/2011
GENERAL
General

• Neutrons have no charge. They interact 

physical collisions with nuclei (target nuc

• A neutron might scatter off the nucleus oGeneral

combine with the nucleus.

• When the neutron combines with a nucle

type of particle might be emitted (e.g., pralpha particle) and/or a “prompt” gamma 
General

• Neutrons, like other indirectly ionizing rad

(e.g., gamma rays), can travel substantiadistances 

General• The probability that a given type of react

occur depends on:

• The neutron energy• The identity of the target nucl
General

Neutron Energies• The types of reactions that are possible a

probability depends on the neutron kinet

• Neutrons are classified according to ene

There is no agreement as to the preciseThere is no agreement as to the precise

classification. The following is approxima

– Thermal (0.025 eV)– Slow (< 10 eV)– Intermediate (10 eV – 100 ke– Fast (>100 keV)
Typical Fate of Neutrons

• Neutrons are born fast. They slow down 

scattering (referred to as moderation) unreach thermal energies. Finally, they are absorbed b

y a tar

get nucleus.

General

y g

Fast neutron 

→ Thermal Neutron 

→ C
Typical Fate of Neutrons

nucleus

nucleus

nucleus

General

nucleus

n

nucleus

nucleus
NEUTRON CROSS SECTION
General

• Each type of interaction can be characte

its cross section.

• The cross section, given the symbol F, dNeutron Cross Sections

the probability of the interaction. 

• It depends on: the nuclide (e.g., H-1 vs H

the neutron energy

• The unit of the cross section is the barn. 

is 10-24 cm2
Types of Interactions 

Scattering: Elastic 

AM(n,n)

AM 

Fel 

Inelastic

AM(n,n’)

AM 

Fin

Proton

AM(n,p)

AN 

Fp 

Al h

AM(

)

A

3

N

Neutron Cross Sections

Al

p

h

a

AM(n,

α

)

A

-

3

N

F

α

Neutron

AM(n,2n)A-1

M

F2n

Neutron-proton

AM(n,np)A-1N 

Fnp

Capture

AM(n,

(

)A+1M 

F

(

Fission 

AM(n,fp)

F

f
Total Cross Section

• The total cross section for a given nuclide 

sum of the individual cross sections for th

nuclide

Neutron Cross SectionsMicroscopic Cross SectionSo far, we have only considered what is knthe microscopic cross section, the cross seatom of a given nuclide.

F

T = 

Fel + 

Finel + 

F

p + 

F

α + 

F2n + 

Fnp + 

F

( + 
Macroscopic Cross Section

The macroscopic cross section is the total section of all the atoms of a given nuclide icentimeter. The units of the macroscopic crsection are cm-1 (i.e., cm

2/cm

3).

Neutron Cross Sections

E

T = N 

FT = (6.02 x 1023) (

F

T) (

D/A

E

T is the total macroscopic cross section (cm-1) 

N is the number of atoms of the nuclide per cm

FT is the microscopic cross section (cm

2

)

D is the density (g/cm

3

)

A is the isotopic mass (g/mole)
Removal Cross Section

The microscopic removal cross section (

F

R

macroscopic removal cross section (

E

R) ar

sometimes used in neutron shielding calcu

Neutron Cross SectionsThe removal cross section is approximately 3/4 of the total cross section. In neutron shielding calculations, we somethe mass attenuation coefficient symbolize
Mass Attenuation Coefficient

According to Schaeffer (1973), the mass atcoefficient (

E

R

/

D) for fast neutrons can be 

approximated with your choice of one of th

following:Neutron Cross Sections

E

R

/

D = 0.19 Z-0.743 cm

2/g (Z 

≤ 8)

= 0.125 Z-0.565 cm

2/g (Z > 8)

E

R

/

D = 0.206 A-1/3 

Z-0.294 ~ 0.206 (

E

R

/

D = 0.21 A-0.58
SCATTERING
Elastic Scattering

• Elastic scattering is a billiard ball type of 

where kinetic energy is conserved, i.e., tkinetic energy is the same before and aft

collision

Scattering

.

n nucleus

Kinetic energy of target nucleus = 0.4 M
Elastic Scattering

• Elastic scattering is the most likely intera

almost all nuclides and neutron energies

• The greatest amount of energy can be trScattering

from the neutron to a target nucleus whelatter has the same mass as the neutronsuch, the lower the atomic mass number target, the more effective it is as a moder

• Moderators (e.g., water, paraffin, plastic, 

graphite) slow neutrons by elastic scatte
Elastic Scattering

• This curve shows the dependence of the 

elastic scattering cross section on neutro

Scattering

H 1 elastic scattering cross section
Inelastic Scattering

• Inelastic scattering is a type of scattering 

collision where kinetic energy is not consThe total kinetic energy was greater befo

collision than after

Scattering

collision than after.

n Excited

nucleus

Kinetic energy of excited target nucleus = 0.3 
Inelastic Scattering

• The remaining energy is given to the targ

nucleus as excitation energy.

• When the scattered nucleus de-excites, Scattering

one or more gamma rays.

• Inelastic scattering is not common. Whe

occur, it is most likely to involve high Z nhigh energy neutrons.

• It is sometimes used as a mechanism to 

moderate very high energy neutrons.
Inelastic Scattering

• This curve shows the dependence of the 

inelastic scattering cross section on neutenergy.

Scattering

Inelastic scattering does not occur below a certain threshold – the minimum energy required to excite the target nucleus

F 56 i l i i i
CHARGED PARTICLE REACTI
General

• The target nucleus absorbs a neutron to 

compound nucleus. The latter then emits charged particle (e.g., proton, alpha part

Charged Particle Reactions• If the final nucleus is left in an excited sta

gamma rays might also be emitted.

• Some reactions are exothermic (no neut

energy threshold) and some are endoth(neutron energy threshold). 
Example Charged Particle Reactions

•

3He(n,p)

3

H

n + He-3 

→ H-3 + H-1 (proton)

L th l t ti 533

Charged Particle Reactions

Large thermal neu

tron cross section: 533

• 10B(n,

α

)

7Li

n + B-10 

→ Li + alpha (α)

Large thermal neutron cross section: 384
Example Charged Particle Reactions

• 32S(n,p)32

P

n + S-32 

→ P-32 + H-1 (pr

Charged Particle Reactions

This is an endothermic reaction with a neenergy threshold of 0.96 MeV. Exothermreactions tend to involve lower Z elemen
Cross Section as a Function of Energy

• These curves show the dependence of S

B-10 charged particle reactions on neutroenergy.

Charged Particle Reactions

S-32 (n,p) B-10 (n, al
CAPTURE REACTIONS
General

• The target nucleus absorbs a neutron. T

resulting nucleus is left in an excited statlatter deexcites with the emission of one “prompt” gamma rays (also known as ca

Capture Reactions

gamma rays (also known as ca

gammas). 

• These gamma rays are often high energy• The product might or might not be stable• This reaction is most likely with thermal n
Example Capture Reaction: H-1(n,

()H-2

•

1H(n,

γ)

2

H

n + H-1 

→ H-2 + gamma (

γ

Capture Reactions• The cross section for thermal neutrons is 

barns. 

• A 2.22 MeV gamma ray is emitted 100% 

time.

• Hydrogen moderates neutrons and abso
Example Capture Reaction: H-1(n,

()H-2

• These curves show the dependence of th

capture reaction with H-1 on neutron ene

Capture Reactions

The probability of the reaction varies with 1/E
FISSION
General

• AM(n,fp)

n + AM → 2 fission products + 2-4 

Fission• The absorption of the neutron produces a 

compound nucleus that gains the kinetic the neutron and the binding energy of the 

• If this energy exceeds the “critical energy 

fission,” the nucleus will split.
Fissile vs. Fissionable

• A fissile nuclide can be induced to fission 

thermal neutrons, e.g., U-233, U-235, Pu241. Most fissile nuclides are alpha emittall have odd atomic mass numbers.

Fission• A fissionable nuclide requires fast neutro

induce fission, e.g., U-238. 

• Fission usually produces two fission prod

The split is asymmetric. With U-235, one product has an atomic mass number in trange while the other is in the 130-150 ra
NEUTRON SHIELDING
The Three Steps

Shielding neutrons involves three steps: 

1. Slow the neutrons

Neutron Shielding

2. Absorb the neutrons3. Absorb the gamma rays
The Three Steps

1. Slow the neutrons• Neutrons are slowed to thermal energie

hydrogenous material: water, paraffin, p

Neutron Shielding• Water can evaporate or leak, paraffin is 

flammable and plastic is expensive.

• To slow down very fast neutrons, iron o

might be used in front of the hydrogenomaterial.
The Three Steps

2. Absorb the neutrons• Hydrogenous materials are also very effective 

absorbing neutrons - the cross section for necapture by H-1 is 0.33 barns. 

Neutron Shielding• Unfortunately, a difficult to shield 2.2 MeV gam

emitted when H-1 absorbs a neutron.

• Boron can be incorporated into the shield – it 

cross section for neutron absorption and only energy capture gamma ray.

• To slow down very fast neutrons, iron or lead 

used in front of the hydrogenous material.
The Three Steps

3. Absorb the gamma rays• Gamma rays are produced in the neutr

by neutron (radiative) capture, inelastic 

Neutron Shielding

scattering, and the decay of activation 
Multipurpose Materials for Neutron Shie

• Concrete, especially with barium mixed 

slow and absorb the neutrons, and shiegamma rays. 

Neutron Shielding• Plastic with boron is also a good multip

shielding material.
Possible Neutron Shields

n

Neutron Shielding

Hydrogenous 

material

Gamma

shield

n

Hi Z moderator 

for fast neutrons

n

Combinat

e.g., borat

concrete 
Neutron Shielding Calculations

Neutron shielding calculations are best doncomputers. Nevertheless, in some limited situations, it is possible to employ a simplisexponential equation similar to that used foNeutron Shieldingexponential equation similar to that used fo

monoenergetic photons.The following equation (Schaeffer 1973) dethe effect of a given shielding material (e.gon fast neutron dose rate. It only works if that least 50 cm of water (or equivalent hydromaterial) behind the shield.
Neutron Shielding Calculations

t

H

O

Neutron Shielding

t

H

2

O

D

D is the dose rate with shieldD0 is the dose rate without shield

t is the shield thickness
Neutron Shielding Calculations

The following equation (modified from one NBS Handbook 63) describes the effect of thickness on the neutron dose rate associawith a radioactive neutron source (e.g., AmNeutron Shielding

D is the dose rate with the shieldD0 is the dose rate without the shield

t is the shield thicknessB is a buildup factor usually assumed to be 
Material

Removal Cross Secti

ER (cm-1)

water 0 103

Neutron Shielding CalculationsCross sections are from NBS Handbook 63Neutron Shielding

water 0.103

iron 0.1576

ordinary concrete 0.0942

barytes concrete 0.0945

graphite 0.0785
NEUTRON INTERACTIONS IN T
Thermal Neutrons (< 0.5 eV)

14N (n, p) 14C

1H (n, () 2H

• Thermal neutrons interact within a short 

Key Neutron Interactions in Tissue

of the tissue surface. The dose to the sutissue in the body is primarily due to the produced in the n-p reaction with 14N.

• The dose to the deeper tissues is due to 

MeV gamma rays from the n-gamma reainvolving H-1.
Thermal Neutrons (< 0.5 eV)

• When large volumes of tissue are consid

(e.g., the size of the torso), the absorbed due to the n-gamma reaction with hydrogbe as much as 100 times the dose due to 

Key Neutron Interactions in Tissue

reaction involving nitrogen. 
Intermediate (0.5-10 keV) and Fast (>10 keV) N

• The largest dose from neutrons at these 

is due to elastic scattering with hydrogen

1H(n, n)

1

H

Key Neutron Interactions in Tissue

• Varying amounts of energy are transferre

hydrogen nucleus (a proton). The latter mtravel up to 10 um in tissue.

• Elastic scattering involving oxygen and to 

lesser extent carbon and nitrogen might contribute 1% to 20% of the total dose.
Intermediate (0.5-10 keV) and Fast (>10 keV) N

• At most, inelastic scattering contributes 

percent of the total dose.

•

Above 20 MeV, nuclear reactions, es

pec

Key Neutron Interactions in Tissue

p 

oxygen become significant and can cont20% of the total dose.

• Spallation, the fragmentation of nuclei, b

significant at 100 MeV where it might co20% of the total dose.
Neutron Interactions and the Quality Fac

• Below 10 keV, the neutron dose in the bo

dominated by the 

1H(n, 

(

)

2H reaction. Si

quality factor (Q) for gamma rays is low a

or less independent of energy so too is t

Key Neutron Interactions in Tissue

or less independent of energy, so too is t

neutron quality factor.

• Above 10 keV, the neutron dose is more 

more dominated by the 

1H(n,n)

1H elastic 

scattering reaction. Since Q for the recoiis greater than Q for gamma rays, the nequality factor increases rapidly above this 
Neutron Interactions and the Quality Fac

• Above 1 MeV, the neutron quality factor b

decrease. This is because the increasing of the recoil proton results in a decreasin

stopping power. As the stopping power

Key Neutron Interactions in Tissue

stopping power. As the stopping power

decreases, so does the proton’s quality f
ctor (Q)

10

Dose Dose primarily

Neutron Interactions and the Quality Fac

Key Neutron Interactions in Tissue

Neutron Energy (MeV)

Quality Fac

05

0.001 0.01 0.1 1 10 

primarily

due to

1H(n, ()2H

due to

1H(n,n)1H

elastic scattering

recoil proton