Interaction of Neutrons

with Matter

2/4/2011 1
GENERAL

2
General
General
• Neutrons have no charge. They interact via
physical collisions with nuclei (target nuclei).

• A neutron might
g scatter off the nucleus or
combine with the nucleus.

• When the neutron combines with a nucleus, some

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

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General
General

• Neutrons, like other indirectly ionizing radiation

(e.g., gamma rays), can travel substantial
distances

• The probability that a given type of reaction will

occur depends on:
• The neutron energy
• The identity of the target nuclide

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General
Neutron Energies

• The types of reactions that are possible and their

probability depends on the neutron kinetic energy.
• Neutrons are classified according to energy.
There is no agreement as to the precise
classification. The following is approximate:

– Thermal (0.025 eV)

– Slow (< 10 eV)
– Intermediate (10 eV – 100 keV)
– Fast (>100 keV) 5
General
Typical Fate of Neutrons

• Neutrons are born fast. They slow down due to

scattering (referred to as moderation) until they
reach thermal energies. Finally, they are
absorbed by y a target
g nucleus.

Fast neutron → Thermal Neutron → Capture

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General
Typical Fate of Neutrons
nucleus

nucleus

nucleus
nucleus
nucleus
neutron
captured
n

nucleus nucleus

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NEUTRON CROSS SECTIONS

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Neutron Cross Sections
General

• Each type of interaction can be characterized by

its cross section.

• The cross section, given the symbol F, describes

the probability of the interaction.

• It depends on: the nuclide (e.g., H-1 vs H-2)

the neutron energy

• The unit of the cross section is the barn. One barn

is 10-24 cm2 9
Neutron Cross Sections
Types of Interactions

Scattering: Elastic AM(n,n)AM Fel , Fs , Fn,n

Inelastic AM(n,n’)AM Finl , Fi , Fn,n’
Proton AM(n,p)AN Fp
Al h
Alpha AM(n,α)
M( )A-3A 3N Fα
Neutron AM(n,2n)A-1M F2n
Neutron-proton AM(n,np)A-1N Fnp
Capture AM(n,()A+1M F(
Fission AM(n,fp) Ff
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Neutron Cross Sections
Total Cross Section
• The total cross section for a given nuclide is the
sum of the individual cross sections for that
nuclide
FT = Fel + Finel + Fp + Fα + F2n + Fnp + F( + Ff

Microscopic Cross Section

So far, we have only considered what is known as

the microscopic cross section, the cross section per
atom of a given nuclide. 11
Neutron Cross Sections
Macroscopic Cross Section
The macroscopic cross section is the total cross
section of all the atoms of a given nuclide in a cubic
centimeter. The units of the macroscopic cross
section are cm-1 (i.e., cm2/cm3).

ET = N FT = (6.02 x 1023) (FT) (D/A)

ET is the total macroscopic cross section (cm-1)
N is the number of atoms of the nuclide per cm3
FT is the microscopic cross section (cm2)
D is the density (g/cm3)
A is the isotopic mass (g/mole)
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Neutron Cross Sections
Removal Cross Section

The microscopic removal cross section (FR) and the

macroscopic removal cross section (ER) are
sometimes used in neutron shielding calculations.

The removal cross section is approximately 2/3 to

3/4 of the total cross section.

In neutron shielding calculations, we sometimes use

the mass attenuation coefficient symbolized ER/D

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Neutron Cross Sections
Mass Attenuation Coefficient

According to Schaeffer (1973), the mass attenuation

coefficient (ER/D) for fast neutrons can be
approximated with your choice of one of the
following:

ER/D = 0.19 Z-0.743 cm2/g (Z ≤ 8)

= 0.125 Z-0.565 cm2/g (Z > 8)

ER/D = 0.206 A-1/3 Z-0.294 ~ 0.206 (A Z)-1/3

ER/D = 0.21 A-0.58 14

SCATTERING

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Scattering
Elastic Scattering

• Elastic scattering is a billiard ball type of collision

where kinetic energy is conserved, i.e., the total
kinetic energy is the same before and after the
collision
collision.

n nucleus

Kinetic energy of target nucleus = 0.4 MeV 16

Scattering
Elastic Scattering

• Elastic scattering is the most likely interaction for

almost all nuclides and neutron energies.

• The greatest amount of energy can be transferred

from the neutron to a target nucleus when the
latter has the same mass as the neutron. As
such, the lower the atomic mass number of the
target, the more effective it is as a moderator.

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

graphite) slow neutrons by elastic scattering.
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Scattering
Elastic Scattering

• This curve shows the dependence of the H-1

elastic scattering cross section on neutron energy.

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H 1 elastic scattering cross section
Scattering
Inelastic Scattering

• Inelastic scattering is a type of scattering

collision where kinetic energy is not conserved.
The total kinetic energy was greater before the
collision than after
after.

n Excited
nucleus

Kinetic energy of excited target nucleus = 0.3 MeV 19

Scattering
Inelastic Scattering

• The remaining energy is given to the target

nucleus as excitation energy.

• When the scattered nucleus de-excites, it emits

one or more gamma rays.
• Inelastic scattering is not common. When it does
occur, it is most likely to involve high Z nuclei and
high energy neutrons.

• It is sometimes used as a mechanism to

moderate very high energy neutrons. 20
Scattering
Inelastic Scattering

• This curve shows the dependence of the Fe-56

inelastic scattering cross section on neutron
energy.
Inelastic scattering
does not occur
below a certain
threshold – the
minimum energy
required to excite
the target nucleus
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F 56 i l i i i
CHARGED PARTICLE REACTIONS

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Charged Particle Reactions
General

• The target nucleus absorbs a neutron to form a

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

• If the final nucleus is left in an excited state,

gamma rays might also be emitted.

• Some reactions are exothermic (no neutron

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

• 3He(n,p)3H

n + He-3 → H-3 + H-1 (proton)

L
Large th
thermall neutron
t cross section:
ti 5330 b
barns.

• 10B(n,α)7Li

n + B-10 → Li + alpha (α)

Large thermal neutron cross section: 3840 barns.
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Charged Particle Reactions
Example Charged Particle Reactions

• 32S(n,p)32P

n + S-32 → P-32 + H-1 (proton)

This is an endothermic reaction with a neutron

energy threshold of 0.96 MeV. Exothermic
reactions tend to involve lower Z elements.

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Charged Particle Reactions
Cross Section as a Function of Energy

• These curves show the dependence of S-32 and

B-10 charged particle reactions on neutron
energy.

S-32 (n,p) B-10 (n, alpha)

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CAPTURE REACTIONS

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Capture Reactions
General

• The target nucleus absorbs a neutron. The

resulting nucleus is left in an excited state. The
latter deexcites with the emission of one or more
“prompt”
prompt gamma rays (also known as capture
gammas).

• These gamma rays are often high energy.

• The product might or might not be stable.

• This reaction is most likely with thermal neutrons.

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Capture Reactions
Example Capture Reaction: H-1(n,()H-2

• 1H(n,γ)2H

n + H-1 → H-2 + gamma (γ)

• The cross section for thermal neutrons is 0.33

barns.

• A 2.22 MeV gamma ray is emitted 100% of the

time.

• Hydrogen moderates neutrons and absorbs them.

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Capture Reactions
Example Capture Reaction: H-1(n,()H-2

• These curves show the dependence of the

capture reaction with H-1 on neutron energy.

The probability of
the reaction varies
with 1/E

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FISSION

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Fission
General

• AM(n,fp)

n + AM → 2 fission products + 2-4 neutrons

• The absorption of the neutron produces a

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

• If this energy exceeds the “critical energy of

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

• A fissile nuclide can be induced to fission by

thermal neutrons, e.g., U-233, U-235, Pu-239, Pu-
241. Most fissile nuclides are alpha emitters and
all have odd atomic mass numbers.

• A fissionable nuclide requires fast neutrons to

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

• Fission usually produces two fission products.

The split is asymmetric. With U-235, one fission
product has an atomic mass number in the 90-110
range while the other is in the 130-150 range. 33
NEUTRON SHIELDING

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Neutron Shielding
The Three Steps

Shielding neutrons involves three steps:

1. Slow the neutrons

2. Absorb the neutrons

3. Absorb the gamma rays

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Neutron Shielding
The Three Steps

1. Slow the neutrons

• Neutrons are slowed to thermal energies with
hydrogenous material: water, paraffin, plastic.

• Water can evaporate or leak, paraffin is

flammable and plastic is expensive.

• To slow down very fast neutrons, iron or lead

might be used in front of the hydrogenous
material.
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Neutron Shielding
The Three Steps
2. Absorb the neutrons
• Hydrogenous materials are also very effective at
absorbing neutrons - the cross section for neutron
capture by H-1 is 0.33 barns.

• Unfortunately, a difficult to shield 2.2 MeV gamma ray is

emitted when H-1 absorbs a neutron.

• Boron can be incorporated into the shield – it has a large

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

• To slow down very fast neutrons, iron or lead might be

used in front of the hydrogenous material. 37
Neutron Shielding
The Three Steps
3. Absorb the gamma rays

• Gamma rays are produced in the neutron shield

by neutron (radiative) capture, inelastic
scattering, and the decay of activation products.

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Neutron Shielding
Multipurpose Materials for Neutron Shields

• Concrete, especially with barium mixed in, can

slow and absorb the neutrons, and shield the
gamma rays.

• Plastic with boron is also a good multipurpose

shielding material.

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 Neutron Shielding
Possible Neutron Shields

Hydrogenous Gamma n
material shield

Combination material
n e.g., borated plastic or
concrete with barium
Hi Z moderator 40
for fast neutrons
Neutron Shielding
Neutron Shielding Calculations

Neutron shielding calculations are best done by

computers. Nevertheless, in some limited
situations, it is possible to employ a simplistic
exponential equation similar to that used for
monoenergetic photons.

The following equation (Schaeffer 1973) describes

the effect of a given shielding material (e.g., steel)
on fast neutron dose rate. It only works if the there is
at least 50 cm of water (or equivalent hydrogenous
material) behind the shield. 41
Neutron Shielding
Neutron Shielding Calculations

t H2O D

D is the dose rate with shield

D0 is the dose rate without shield

t is the shield thickness 42

Neutron Shielding
Neutron Shielding Calculations
The following equation (modified from one in from
NBS Handbook 63) describes the effect of shield
thickness on the neutron dose rate associated
with a radioactive neutron source (e.g., AmBe).

D is the dose rate with the shield

D0 is the dose rate without the shield

t is the shield thickness

B is a buildup factor usually assumed to be 5 43

Neutron Shielding
Neutron Shielding Calculations
Cross sections are from NBS Handbook 63
Removal Cross Section
Material
ER (cm-1)
water 0 103
0.103

iron 0.1576

ordinary concrete 0.0942

barytes concrete 0.0945

graphite 0.0785
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NEUTRON INTERACTIONS IN TISSUE

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Key Neutron Interactions in Tissue
Thermal Neutrons (< 0.5 eV)
14N (n, p) 14C
1H (n, () 2H

• Thermal neutrons interact within a short distance

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

• The dose to the deeper tissues is due to the 2.2

MeV gamma rays from the n-gamma reaction
involving H-1.
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Key Neutron Interactions in Tissue
Thermal Neutrons (< 0.5 eV)
• When large volumes of tissue are considered
(e.g., the size of the torso), the absorbed dose
due to the n-gamma reaction with hydrogen can
be as much as 100 times the dose due to the n-p p
reaction involving nitrogen.

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Key Neutron Interactions in Tissue
Intermediate (0.5-10 keV) and Fast (>10 keV) Neutrons

• The largest dose from neutrons at these energies

is due to elastic scattering with hydrogen.
1H(n, n)1H
• Varying amounts of energy are transferred to the
hydrogen nucleus (a proton). The latter might
travel up to 10 um in tissue.

• Elastic scattering involving oxygen and to a

lesser extent carbon and nitrogen might
contribute 1% to 20% of the total dose. 48
Key Neutron Interactions in Tissue
Intermediate (0.5-10 keV) and Fast (>10 keV) Neutrons

• At most, inelastic scattering contributes a few

percent of the total dose.

• Above 20 MeV, nuclear reactions, especially

p y with
oxygen become significant and can contribute
20% of the total dose.

• Spallation, the fragmentation of nuclei, becomes

significant at 100 MeV where it might contribute
20% of the total dose.
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Key Neutron Interactions in Tissue
Neutron Interactions and the Quality Factor

• Below 10 keV, the neutron dose in the body is

dominated by the 1H(n, ()2H reaction. Since the
quality factor (Q) for gamma rays is low and more
or less independent of energy
energy, so too is the
neutron quality factor.

• Above 10 keV, the neutron dose is more and

more dominated by the 1H(n,n)1H elastic
scattering reaction. Since Q for the recoil proton
is greater than Q for gamma rays, the neutron
quality factor increases rapidly above this energy.
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Key Neutron Interactions in Tissue
Neutron Interactions and the Quality Factor

• Above 1 MeV, the neutron quality factor begins to

decrease. This is because the increasing energy
of the recoil proton results in a decreasing
stopping power. As the stopping power
decreases, so does the proton’s quality factor.

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 Key Neutron Interactions in Tissue
Neutron Interactions and the Quality Factor
10
ctor (Q)

Dose Dose primarily

Quality Fac

primarily due to
5 due to 1H(n,n)1H
1H(n, ()2H elastic scattering
recoil proton

0
0.001 0.01 0.1 1 10 100
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Neutron Energy (MeV)