Neutron Interactions
Part I
Rebecca M. Howell, Ph.D.
Radiation Physics
rhowell@mdanderson.org
B1.4580
November 2010
Why do we as Medical Physicists care
about neutrons?
• Neutrons in Radiation Therapy
• Neutron Therapy
• Contamination Neutrons on X-Ray Therapy
• Contamination Neutrons in Proton Therapy
• Unwanted
patient dose
• Shielding
Considerations
• Neutron Dose
• The above will be discussed in lecture #2.
• Today’s focus will be general neutron interactions
Outline – Neutron Interactions
• General properties
• Neutron Reaction Cross Sections
• Neutron Interactions
General Properties
• Neutrons are Neutral
• Can Not interact by coulomb forces
• Can travel through several cm of material without
interacting.
• Neutrons interact with nucleus of absorbing
material (no not interact with orbital
electrons).
Reaction Cross Sections
Used to describe neutron interaction probabilities.
Reaction Cross Sections
• A neutron reaction cross section quantitatively
describes the probability of a particular interaction
occurring between a neutron and matter.
• When the reaction cross section is defined
microscopicly on per nucleus, it is denoted by s
and has S.I. Units = cm2
• Common unit for reaction neutron cross sections is the
barn (10-24cm2).
• Reaction cross sections are BOTH energy and
interaction type dependent.
Reaction Cross Sections
• Energy and interaction type dependent - tabulated
as a function of energy and interaction type.
Reaction Cross Sections
• Macroscopic cross section, S, probability per unit path
length that a particular type of interaction will occur.
S  Ns
• s = microscopic cross section, cm2
• N = number of nuclei per unit volume, nuclei/cm3
• All processes can be combined to calculate Stotal,
probability per unit path length that any type of interaction
will occur.
STotal  Sscatter  Srad .capture  .....
Exponential Attenuation
• Neutrons are removed
exponentially from a
collimated neutron beam
by absorbing material.
I  I oe
 Stotal t
stotalN
where
Io
I
N = number of absorber atoms
per cm3 (atomic density)
s = the microscopic cross
section for the absorber, cm2
t = the absorber thickness, cm
Exponential Attenuation
Example
• In an experiment designed to measure the
total cross section of lead for 10 MeV
neutrons, it was found that a 1 cm thick lead
absorber attenuated the neutron flux to
84.5% of its initial value.
• The atomic weight of lead is 207.21, and its
density is 11.3 g cm-3.
• Calculate the total cross section from these
data.
Exponential Attenuation
Example
• Rearrange/Solve the general attenuation equation
for s:
 I0 
log 
I 

s

Nt
Calculate N, the atomic density of lead:
11.3g 6.031023 atoms 1 mole


3
cm
mole
207.21g
atoms
3.291022
cm3
log1.18
 5.11024 cm2  5.1 barn
22 atoms
1cm
3.2910
3
cm
Neutron Mean Free Path, l
l
1
STotal
Units: cm
• Slow (low energy) neutrons
• l is on the order of 1cm or less
• For fast (high energy) neutrons
• l may be tens of centimeters
Neutron Mean Free Path, l
Example
• Calculate the mean free path for the previous
example.
s  5.110 cm
24
l
1
STotal
2
atoms
N  3.29 10
cm 3
1

 0.168cm
sN
22
Some preliminary
background
compound nucleus model
and resonance
Compound Nucleus Model
Multi-step Reaction
• Incident neutron and target nucleus fuse together,
then by successive nucleon-nucleon collisions within
the combined system, the reaction energy becomes
shared among many nucleons. A + a  C
• Eventually an equilibrium occurs and the compound
nucleus exists in an excited state (10-16-10-18 seconds).
A + a  C*
• Excitation is followed by deexcitation when a single
nucleon or group of nucleons acquires enough
energy to escape. A + a  C  B + b
Compound Nucleus Model
Multi-step Reaction
The energy and nature of outgoing particles is
determined by properties of the excited compound
nucleus and NOT by the properties of the colliding
particles from which it was formed.
Compound Nucleus Model
• Note: if the excitation energy is close to the
threshold energy, the compound nucleus will decay
by emitting only g-rays or the competing decay
mode of internal conversion of electrons.
• Recall: electron capture is a process that competes with g-ray
emission in which the energy of an excited nuclear state is
transferred to an atomic electron (typically K or L).
Resonance
• In this example, at ≈ 250 keV, the neutron energy is such that
the compound nucleus 7Li is formed at an excitation which
corresponds exactly to one of its higher states or natural
frequencies.
Peak is due to
“resonance” in initial
fusion process of
the neutron with 6Li
target.
Resonance
• At higher energies x-section may have large peaks.
• Peaks = resonances
• Occur at neutron energies where reactions with nuclei
are enhanced
• A resonance will
occur if the energy
of the incident
neutron is close to
the energy of an
excited state of the
compound nucleus
Rinard,
Fig. 12.3
Neutron
Classifications and Interactions
by energy
Classification of Neutrons by Energy
There are three energy categories of neutrons (NCRP-38):
1. Thermal neutrons are in thermal equilibrium with the
medium they are in. The average energy of thermal
neutrons is typically below 1eV, depending on temperature.
The most probable velocity for thermal neutrons is 2200
meters per second at 20.44oC. This velocity corresponds
to an energy of 0.0253eV.
2. Intermediate Energy Neutrons are classified as having
intermediate energy range from above 1eV to tens of keV.
1. Fast Neutrons are classified as having energies above the
intermediate neutrons.
Classification of Neutrons by Energy
The classification of neutrons by energy is somewhat
dependent on the reference text. Some sources may
include an epithermal category while others only
include fast and slow (thermal).
Category
Fast
Intermediate
Epithermal
Thermal
Energy Range
> 500 keV
10 keV – 500 keV
0.5 eV – 10 keV
< 0.5 eV
0.5 eV
Cd-cutoff energy:
sharp drop
occurs in Cd
absorption cross
section at 0.5 eV
Neutron Interactions
are Energy Dependent
Overview of Neutron Interactions
Scatter and Absorption
Total
Scatter
Elastic Inelastic
Scatter Scatter
(n,n)
(n,n’)
Absorption
Nonelastic
Processes
(n,n’3a)
Sometimes shown
as (n,ng)
Also called
“neutron capture”
(n,n’4a)
(n,n’etc)
Electro- Charged
magnetic
(n,p)
(n,g)
(n,a)
(n,d)
(n,etc)
Sometimes
called
“radiative”
capture
Neutral Fission
(n,f)
(n,2n)
(n,3n)
(n,4n)
(n,xn)
Sometimes called
“transmutation”
Boxes shaded in light blue follow the compound nucleus model.
General Neutron Interactions
Scattering and Absorption
Scatter
Absorption
• When neutron is elastically or
• When neutron is absorbed by
inelastically scattered by nucleus
nucleus, a wide range of radiations
speed and direction change, but
can be emitted or fission can be
nucleus is left with same number
induced.
of protons and neutrons as
before the interaction.
• Different the number of protons and/or
neutrons than before the interaction.
• Elastic Scatter (n,n)
• Inelastic Scatter (n,n’)
Electromagnetic
Neutral
• (n,g)
•
•
•
•
Charged
•
•
•
•
(n,p)
(n,a)
(n,d)
(n,etc)
(n,2n)
(n,3n)
(n,4n)
(n,etc)
Fission
• (n,f)
Neutron Interactions are
Energy Dependent
• Fast neutrons are most likely to undergo scatter
interactions with atoms in their environment.
• Elastic Scatter – dominate for lower energy fast neutrons
• Inelastic Scatter - above 1-Mev
• Lower energy neutrons (thermal or near thermal)
are likely to undergo absorption reactions with
atoms in their environment.
Neutron Scatter
• Elastic Scatter – Kinetic Energy Conserved
• More likely in low Z materials
• More likely at lower energies, < 1MeV
• Maximum amount of energy that can be lost is function of target
nuclei mass.
• Larger cross sections
• Inelastic Scatter – Kinetic Energy NOT Conserved.
•
•
•
•
•
More likely in high Z materials
More likely at higher energies E > 1MeV
Can loose large amounts of energy in one collision
Smaller cross sections
Threshold Energy
Neutron Elastic Scatter (n,n)
• Elastic scattering is the most likely interaction
between (lower energy) fast neutrons and low Z
absorbers.
• Billiard ball type collision
•
•
Direct (head-on) collision – More energy transferred
Indirect (grazing) Collision – Less Energy transferred
• Kinetic energy and momentum are conserved
• Light recoiling nucleus can cause high LET tracks
Kinematics of Neutron Elastic Scattering
• For incoming neutrons conservation
of energy and momentum in the
center-of-mass coordinate system
gives the following relation for
energy of the recoil nucleus:
• Convert to laboratory system
(general target nucleus is at rest):
• Recoil nucleus energy in terms
of its own angle of recoil.

2A
1  cosEn
ER 
2
1  A

4A
2
ER 
cos
 En
2
1  A
Knoll fig 15-12
Note: assume incoming neutrons have nonrelativistic kinetic energy (En<939MeV),
Definition of Symbols
• A= mass of target nucleus (laboratory system)
• En = incoming neutron kinetic energy (laboratory system)
• ER = recoil nucleus kinetic energy (laboratory system)
•
  scattering angle of the recoiled neutron in the center-ofmass coordinate system
•
  scattering angle of the recoiled neutron in the lab
coordinate system
Kinematics of Neutron Elastic
Scattering
• Equation demonstrates that energy given to recoil
nucleus is determined by scattering angle:


4A
2
ER 
cos  En
2
1  A
Elastic Scatter
Grazing Angle Encounter
• For grazing angle encounter, the neutron is only
slightly deflected and the recoil target nucleus is
emitted almost perpendicular to the incident
neutron, ≈90.
0
• Energy of recoil nucleus :


4( A)
2
ER 
cos 90 En
2
1  A
• For a grazing hit almost no energy goes to recoil
nucleus, regardless of mass of the target nuclei.
Elastic Scatter
Direct Head-On Encounter
• For head-on direct collision between an incoming
neutron and a target nucleus, the recoil is emitted
in almost the same direction as the incident
neutron, ≈0.
• Energy of recoil nucleus :
1


4( A)
2
ER 
cos 0 En
2
1  A
• For a direct hit, energy that goes
to recoil nucleus, depends on
mass of the target nuclei.
ER
4( A)

2
En 1  A
Maximum Fractional Energy Transfer in
Neutron Elastic Scattering
Target ER max  4( A)
2
E


1

A
Nucleus n
1H
1
2H
8/9=0.889
3He
3/4=0.750
4He
16/25=0.640
12C
48/169=0.284
16O
64/289=0.221
For direct head-on collisions:
• The maximum fractional
energy transfer increases as
the mass of target nuclei
decreases:
• Nuclei with lower mass are
more effective on a “per
collision” basis for slowing
down neutrons!
Energy Distribution of Recoil Nuclei
(from Elastic Neutron Scatter)
• All scattering angles are allowed.
• However, for most target nuclei, forward and
backward scattering are somewhat favored.
• Actual energy distribution for recoil nuclei is a
continuum between the two extremes.
Neutron Inelastic
Scatter (n,n’ or (n,ng)
• Inelastic Scatter - neutron is captured by target nucleus and is
reemitted (may not be same neutron) along with g-ray.
Inelastic scatter follows the compound nucleus model:
1. Neutron collides with nucleus and fuse together to form a combined
system.
2. By successive nucleon-nucleon collisions within the combined
system, the reaction energy becomes shared among many
nucleons
3. Eventually an equilibrium occurs and the compound nucleus exists
in an excited state.
4. Excitation energy is emitted as gamma photon, g can have
substantial energy.
5. Neutron (not necessarily the incoming neutron) is emitted.
Neutron Inelastic Scatter
• Inelastic Scatter = Threshold Phenomenon
• Infinite threshold for H (inelastic can not occur)
• 6 MeV Threshold for O
• 1 MeV Threshold for Ur
• Cross section increases with increasing energy.
• s ≤1 barn for low Energy neutrons.
• s approaches geometric cross-section of target
nucleus at high energies i.e. inelastic scatter is
dominate interaction mechanism at higher energies.
General Neutron Interactions
Nonelastic Processes
(n,n’3a)
(n,n’4a)
(n,n’etc)
Nonelastic Processes
• Similar to inelastic scatter in that the process follows a
compound nucleus model and that there is a recoil neutron.
• Different from inelastic scatter because instead of emitting grays, additional secondary particles can be emitted (in
addition to scattered neutron).
• Nucleus has different number of p+ and no after interaction.
• Different from absorption because neutron is not absorbed, a
scattered neutron is emitted (may not be the same one that
entered reaction).
• Sometimes called nonelastic scatter.
Nonelastic verses Inelastic
• Both non-elastic and inelastic scatter follow a
compound nucleus model.
• Whether the compound nucleus will deexcite via non-elastic or inelastic scatter is
determined by the energy of the incident
neutron…..
if the energy of the incident neutron is very close to
the threshold energy, de-excitation occurs by
emission of gamma rays rather than by additional
particle emissions i.e. inelastic scatter is favored
over non-elastic scatter.
Absorption (Neutron Capture)
• Low energy neutrons (thermal or near thermal) are
likely to undergo absorption reactions.
• In this energy range, the absorption cross-section of
many nuclei, has been found to be inversely
proportional to the square root of the energy of the
neutron.
• one-over-v law for slow neutron absorption
1
1
s

E 
Thermal Neutron Absorption
Cember fig 5.23
Thermal Neutron Absorption
Cross Sections
Halflife
Cross
section
[barn atom-1]
Isotope
Abundance
Isotope
Produced
23Na
100%
24Na
15 h
0.93
31P
100%
32P
14.3 d
0.18
41K
6.9%
42K
12.4 h
1.46
58Fe
0.33%
59Fe
45.1 d
1.15
59Co
100%
60Co
5.26 y
37
197Au
100%
198Au
2.69 d
99
10B
19.8%
7Li
Stable
3837
B (all
Cd (all
isotopes)
• If the cross section at
E0 is s0, then the
cross section for any
other neutron (within
the validity of the 1/v
law is given by:
759
isotopes)
113Cd
• Thermal neutron
cross sections are
given for neutrons
whose energy is
0.025eV.
12.3%
114Cd
Stable
20000
2450
E0
s 0
 
s0 
E
Neutron Activation
• Neutron activation is the production of a
radioactive isotope by absorption of a neutron.
• Activation reactions follow absorption reactions.
Examples:
• 14N(n,p)14C
• 10B(n,a)7Li
• 113Cd(n,g)114C
Activation
Good and Bad
• Byproducts of activation can have
substantial energy:
• Good: These byproducts can be
measured. This technique is one
of the methods most frequently
used for neutron detection.
• Detection class:
We will discuss
neutron detection
via activation foils.
• Bad: These byproducts can pose
a radiation hazard.
• Must be
considered in
neutron shielding
design.
“Most Common”
Neutron Interactions
in Tissue
Neutron Interactions with Tissue
• The type of interaction and the amount of dose
deposited in the body is strongly dependent on
neutron energy and absorbing material.
• The most common elements in the human body are
Hydrogen, Carbon, Nitrogen, and Oxygen.
• Neutrons are indirectly ionizing and but give rise to
densely ionizing (high LET) particles: recoil
protons, a-particles, and heavier nuclear fragments
• These particles then deposit dose in tissue.
Fast Neutron Interactions in Tissue
• Higher energy neutrons interact with carbon
and oxygen via nonelastic processes and
result in the release of charged a-particles,
(n,n’3a) and (n,n’4a).
• These a-particles then deliver dose to tissue
Fast Neutron Interactions in Tissue
• Recoil a-particles
 A neutron interacts with a Carbon
 A neutron interacts with an Oxygen
nucleus (6 protons and 6 neutrons),
nucleus (8 protons and 8 neutrons)
resulting in three a-particles.
, resulting in four a-particles.
(Hall, Fig 1.10)
(Hall, Fig 1.10)
Intermediate Neutron Interactions in Tissue
• Intermediate energy neutrons primarily interact with
hydrogen nuclei via elastic scatter.
• Dominant mechanism of energy transfer in soft
tissues
3 Reasons
1. Hydrogen is the most abundant
atom in tissue.
2. A proton and a neutron have
similar mass, 938 MeV/cm2
versus 940 MeV/cm2.
3. Hydrogen has a large elastic
scatter cross-section for
neutrons.
Thermal Neutron Interactions in Tissue
• Absorption is the dominant interaction mechanism
for thermal neutrons in tissue.
• Absorption is followed by activation.
• Activation decay products deliver dose to tissue.
Thermal Neutron Interactions in Tissue
• The major component of dose from thermal neutrons is
a consequence of the 14N(n,p)14C + 0.62 MeV
• 0.04 MeV to recoil nucleus (local absorption)
• 0.58 MeV to proton (range of ~10-6 m  local absorption)
• Dominant energy transfer mechanism in thermal and
epithermal region in body
• Kerma = dose
• Another thermal neutron interaction of some
consequence is the 1H(n,g)2H + 2.2 MeV
• 2.2 MeV to gamma (nonlocal absorption)
• Small amount of energy to deuterium recoil (local absorption)
• Kerma  dose (non-local absorption)
Summery
Neutron Interactions with Tissue
The amount of dose deposited in the body is strongly
dependent on neutron energy.
• Fast neutrons interact with carbon and oxygen via nonelastic
processes and result in the release of charged a-particles, (n,n’3a)
and (n,n’4a). These a-particles then deposits dose to tissue.
• Intermediate energy neutrons primarily interact with hydrogen nuclei
via elastic scatter. The recoil proton then deposits dose in tissue.
• Absorption is the dominant interaction mechanism for thermal
neutrons in tissue and is followed by activation. The major
component of dose from thermal neutrons is a consequence of the
14N(n,p)14C which results in a 0.58 MeV proton.
References/Acknowledgements
• Glenn Knoll. Radiation Detection and
Measurement, 4th Ed. (2010)
• Herman Cember. Introduction to Health
Physics 3rd Ed. (1996)
• Eric J. Hall. Radiobiology for the Radiologist
5th Ed. (2000)
• Frank H. Attix. Introduction to Radiological
Physics and Radiation Dosimetry. (1986)