4. Elastic Scattering
• Both kinetic energy and momentum are
conserved.
• Target nucleus remains in the ground state.
• No change in reacting particles.
• Typically occurs when a neutron interacts
with a light nucleus such as hydrogen.
• Can be modeled as a billiard ball collision
between a neutron and a nucleus.
• This is the type of reaction that mostly
helps fast neutrons to be slowed down to
low energies in a reactor.
n
X
n
X
After collision
Before collision
No change in reacting
particles
Neutron interactions
4
Nuclear Reactions
EgyE 225: Nuclear Energy
5. Inelastic Scattering
• Only the momentum is conserved.
• Rebounding nuclide is left in an excited
energy state.
• Total kinetic energy is decreased before and
after the collision. The difference accounts
for the energy of excitation.
• The excited nucleus subsequently de-excites
by emitting -radiation.
• Occurs when the neutron has KE that
exceeds the excitation energy of the nucleus.
γ-ray
n
X*
n
X
∗
∗
X* is in an excited state
Neutron interactions
After collision
Before collision
5
Nuclear Reactions
EgyE 225: Nuclear Energy
6. γ-ray
n
Y
n
X
Neutron interactions
Radiative capture
• The neutron is absorbed by the target
nucleus to form the next higher isotope
(of mass A+1), in an excited state of
energy.
• The new isotope de-excites by emitting
-rays.
• Neutron is lost in this reaction.
After collision
Before collision
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7. Charge and neutron production
• Charge production: Interaction results
in production of charged particles such
as proton, deuteron or alpha particles.
• Neutron production: Interaction results
in production of more neutrons, 2n, 3n
• These are generally threshold
reactions, which means that a certain
minimum neutron energy is required
for the reaction to occur.
n X
b = , p, 2n, 3n
Y
n
b
Neutron interactions
After collision
Before collision
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8. Fission reaction
• Most important reaction for nuclear
energy.
• When a neutron hits a heavy nuclide
like U-235, the neutron gets absorbed
in the heavy nuclide that gets
energetically agitated (or excited).
• If the new energy state of the heavy
nuclide is sufficient for it to split, then it
can split to cause fission.
• Most neutrons produced in fission are
fast, with an average energy of 2 MeV.
Neutron interactions
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9. Definition: Measure of the probability that a neutron interaction will
occur
Cross-sectional area of a target atom as “seen” by an
incident particle (projectile).
Unit: barn, b = 10-24 cm2 = 10-28 m2
700 m/s 1,000 m/s
Microscopic cross section,
Nuclear cross section
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11. Material
Cross-sections in barns
Thermal neutrons
(E = 0.0253 eV)
Fast neutrons
(E > 100 eV)
Fission Capture Fission Capture
Fissile
92-U-233 528.45 45.76 2.7323 0.27176
92-U-235 585.086 98.6864 1.9041 0.55549
94-Pu-239 747.401 270.329 1.7973 0.49614
Fertile
92-U-238 0.00001177 2.71692 0.042758 0.33188
90-Th-232 0.0 7.4 0.010193 0.38157
Clad
40-Zr 0.185396 0.0265766
Steel 3.08668 0.0170228
Coolant
Light Water 0.664 0.00051554
Heavy Water 0.0013 0.00011459
11-Na-23 0.528 0.0027511
Control Rod
5-B-10 3840.0 2.73462
48-Cd 2524.15 0.266766
Fission Products
54-Xe-135 2636300.0 0.0059985
36-Kr-83 207.667 0.235944
62-Sm-149 40144.3 1.91883
Cross-sections
of some
important
reactor
materials
Nuclear cross section
11
Nuclear Reactions
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12. Figure: Typical neutron
microscopic cross
section vs neutron
energy.
Photo reference: US
DOE Handbook.
Nuclear cross section
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13. Neutron classification based on spectrum regions
Classification Neutron Energy, eV Speed, m/s
Fast Greater than 105 Greater than 4.4106m/s
Intermediate
(Resonance/ Epithermal)
1 - 105 1.38104m/s - 4.4106m/s
Slow
(Thermal)
Less than 1 Less than 1.38104m/s
Nuclear cross section
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14. Nuclear cross section
Depends on target material and energy of incident neutron
1E-1
1E+0
1E+1
1E+2
1E+3
1E-11 1E-8 1E-5 1E-2 1E+1 1E+4
Cross
section
(barns)
Incident Energy (MeV)
H-1 (total)
C-14 (total)
1E-1
1E+1
1E+3
1E+5
1E-11 1E-8 1E-5 1E-2 1E+1
Cross
section
(barns)
Incident Energy (MeV)
B(n,a)Li
B-10 (total)
https://www-nds.iaea.org/exfor/endf.htm
1E-2
1E+0
1E+2
1E+4
1E+6
1E-11 1E-8 1E-5 1E-2
Cross
section
(barns)
Incident Energy (MeV)
Cd-109 (total)
Cd-109 (n,g)
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15. Atom density
Atom density is the number of atoms of a given type per unit
volume of the material.
atom density (atom/cm3)
atomic mass (g/mole)
mass density (g/cm3)
Avogadro’s number particles/mole
Nuclear cross section
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16. Macroscopic cross section,
– Interaction of neutron with a certain volume of material depends
not only on the microscopic cross section of a given nuclei but also
on the number of nuclei within that volume.
– Macroscopic cross section () is the probability of a given reaction
to occur within a unit distance traveled by a neutron:
where macroscopic cross section (cm-1)
atom density (atoms/cm3)
microscopic cross section (cm2)
Nuclear cross section
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17. Macroscopic cross section,
– The average distance traveled by a neutron before interaction is
known as the mean free path, .
– The mean free path has a unit of distance and is related to the
macroscopic cross section:
•
Nuclear cross section
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18. Effects of temperature on cross section
• Microscopic cross sections provided on most charts and tables are
measured for a standard neutron speed of 2200 m/s, which
corresponds to an ambient temperature of 20C.
• The following formula is used to correct microscopic cross sections
for temperature:
where microscopic cross section corrected for temperature
microscopic cross section at reference temperature
temperature for which corrected value is being calculated (in K)
reference temperature (in K)
Nuclear cross section
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19. Atoms do not interact preferentially
with neutrons from any particular
direction.
Photo reference: Lamarsh (2001)
• Neutron flux is the total path length covered
by all neutrons in one cm3 during 1 s:
where neutron flux (n/cm2-s)
neutron density (n/cm3)
neutron speed (cm/s)
• Neutron intensity ( ) is the number of
neutrons per unit area and time (n/cm2-s)
falling on a surface perpendicular to the
direction of the beam.
Neutron Flux,
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EgyE 225: Nuclear Energy
20. • Reaction rate is the number of interactions occurring in a
unit volume of a material per unit time:
where reaction rate (reactions/cm3-s or cm-3s-1)
neutron flux (n/cm2-s)
macroscopic cross section (cm-1)
atom density (atoms/cm3)
microscopic cross section (cm2)
Reaction rate
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21. Neutron slowing down and thermalization
• Fission neutrons are produced at an average
energy of 2 MeV.
• Neutrons slow down as a result of numerous
scattering reactions with a variety of target nuclei.
• After a number of collisions, the speed of a
neutron is reduced to such an extent that it has
approximately the same KE as the particles of the
medium in which it is interacting.
• This energy, ~0.025 eV at 20C, is referred to as the
thermal energy.
• Thermal neutrons are those with energies that
have been reduced to this region (<1 eV).
Neutron Migration:
r1 is the distance from neutron source
(S) to a point where it is thermalized (T),
r2 is the distance from T to absorption
point (A).
Neutron moderation
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22. Neutron slowing down and thermalization
• A moderator is a material used to slow down or
thermalize neutrons.
• An ideal moderator should have the following
nuclear properties:
• Large scattering cross section
• Small absorption cross section
• Large energy loss per collision
Neutron Migration:
r1 is the distance from neutron source
(S) to a point where it is thermalized (T),
r2 is the distance from T to absorption
point (A).
Neutron moderation
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23. Neutron slowing down and thermalization
• A convenient measure of energy loss per collision is the average
logarithmic energy decrement,
where average initial neutron energy
average final neutron energy
• On the average, a neutron loses a fixed fraction of its energy per scattering
collision.
• is constant for a given material and does not depend on the initial
neutron energy.
Neutron moderation
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24. Neutron slowing down and thermalization
• The total number of collisions ( ) necessary for a neutron to lose a given
amount of energy can be obtained from :
where initial neutron energy
final (lower) neutron energy
Neutron moderation
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25. Neutron slowing down and thermalization
• In addition to the ability of a material to slow neutrons down, it is also
important to consider its scattering and absorption properties.
• The macroscopic slowing down power (MSDP) is the product of the
logarithmic energy decrement and the macroscopic cross section ( ) for
scattering in the material:
• The moderating ratio (MR) is the ratio of the MSDP to the macroscopic
cross section for absorption ( ):
Neutron moderation
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26. Neutron slowing down and thermalization
Material 𝒄 MSDP MR
H2O 0.927 19 1.425 62
D2O 0.510 35 0.177 4830
Helium 0.427 42 51
Beryllium 0.207 86 0.154 126
Boron 0.171 105 0.092 0.0086
Carbon 0.158 114 0.083 216
Moderating properties of material
Neutron moderation
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27. References
• Lamarsh, J. R., and Anthony J. Baratta. Introduction to
Nuclear Engineering. 3rd ed. Englewood Cliffs, NJ: Prentice
Hall, 2001.
• Lewis, E. E., Fundamentals of Nuclear Reactor Physics,
Academic Press, 2008.
• Turner, J.E., Atoms, Radiation and Radiation Protection (3rd
ed.). Weinheim: Wiley-VCH, 2007.
Research Reactors 27
