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Neutron interaction with matter
1) Introduction 2) Elastic scattering of
neutrons 3) Inelastic scattering of neutrons 4)
Neutron capture 5) Other nuclear reactions 6)
Spallation reactions, hadron shower
Important cross sections of nuclear interactions
Mostly neutron loses only part of energy
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Introduction
Neutron has not electric charge ? interaction
only by strong nuclear interaction
Magnetic moment of neutron ? interaction by
electromagnetic interaction, mostly

negligible influence
Different energy ranges of neutrons Ultracold
E lt 10-6 eV Cold and very cold E (10-6 eV
0,0005 eV) Thermal neutrons (0,002 eV 0,5
eV) neutrons are in thermal equilibrium with
neighborhood, Maxwell distribution of velocities,
for 20oC is the most probable velocity v 2200
m/s ? E 0,0253 eV Epithermál neutrons and
resonance neutrons E (0,005 eV 1000
eV) Cadmium threshold 0,5 eV - with
higher energy pass through 1 mm of Cd Slow
neutrons E lt 0,3 eV Fast neutrons E
(0,3 eV 20 MeV) Neutrons with high energies
E (20 MeV 100 MeV) Relativistic neutrons 0,1
10 GeV Ultrarelativistic neutrons E gt 10 GeV
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Elastic scattering of neutrons
Most frequent process used for kinetic energy
decreasing (moderation) of neutrons
Moderation process of set of independent
elastic collisions of neutron on nuclei
Usage of nucleus reflected during scattering for
neutron energy determination
Maximal transferred energy (nonrelativistic case
of head-head collision)
MCL pn0 pA - pn
ECL En0KIN EAKIN EnKIN ? pn02/2mn
pA2/2mA pn2/2mn
MCL pn2 pA2 2pApn0 pn02 ? mApn2
mApA2 2mApApn0 mApn02
ECL
mApn2 - mnpA2
mApn02
We subtract equation 0 mApA2 mnpA2
2mApApn0 ? mApA mnpA 2mApn0
The heavier nucleus the lower energy can neutron
transferred to it
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Usage of hydrogen (? neutron scattering angle,
? proton reflection angle) mp mn
pn pn0?cos? ? En En0?cos2?
pp pn0?sin? ? Ep En0?sin2?
? p/2-?
pp pn0?cos? ? Ep En0?cos2?
pn pn0?sin? ? En En0?sin2?
For nucleus
Elastic scattering in our case particle 1
neutron particle 2 proton, generally nucleus
Dependency of energy transferred to proton on
reflected angle
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Small expose with derivation of relation between
laboratory and centre of mass angles
Laboratory coordinate system
Centre of mass coordinate system
Derivation of relation between scattering angles
at centre of mass and laboratory coordinate
systems
Relation between velocity components to the
direction of beam particle motion is
Relation between velocity components to the
direction perpendicular to beam particle motion
Ratio of these relations leads to
For elastic scattering is valid
derive!
Insertion
Equation can be rewrite to
and then
and required relation is valid
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Angular distribution of scattering neutrons at
centre of mass coordinate system
Relation between angular distribution and energy
distribution
We introduce and express distribution of
transferred energy
We determine appropriate differential dEA
Introduce for dEA
(it is valid approximately for protons up to En0
lt 10 MeV)
Energy distribution of reflected protons for En0
lt 10 MeV
Efficiency e is given
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Coherent scattering diffraction on lattice
Magnitude of energy neither momentum and wave
length of neutrons are not changed
Diffraction of neutrons on crystal lattice is used
Mentioning Bragg law n?? 2d?sin T
0,0288 eV½nm for En in eV
Lattice constants are in the order 0,1 1 nm ?
Neutron energy in the orders

of meV up to eV
E eV 0,001 0,005 0,01 0,1 1 10 100 1000
? nm 0,91 0,41 0,29 0,091 0,029 0,0091 0,0029 0,00091
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Inelastic neutron scattering
Competitive process to elastic scattering on
nuclei heavier than proton
Part of energy is transformed to excitation ?
accuracy of energy determination is given by
their fate
Its proportion increases with increasing energy
Nuclear reactions of neutrons
Neutron capture (n,?)
High values of cross sections for low energy
neutrons
Exothermic reactions
Released energy allows detection
Cross section of reaction 139La(n,?)140La
157Gd(n,?) for thermal neutrons cross section
is biggest s 255 000 barn
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Reaction (n, 2n), (n,3n), ...
Endothermic (threshold) reactions
Threshold reactions Bi(n,Xn)Bi
Examples of threshold reactions
197Au(n,2n)196Au 197Au(n,4n)194Au
27Al(n,a)24Na
Reactions (n,d), (n,t), (n,a) ...
Reactions used for detection of low energy
neutrons (exoenergy)
(two particle decay of compound nucleus at rest,
nonrelativistic approximation)
10B(n,a)7Li Q 2,792 and 2,310 MeV, Ea MeV,
ELi MeV sth 3840 b 1/v up to 1 keV
6Li(n,a)3H Q 4,78 MeV, Ea 2,05 MeV, EH
2,73 MeV sth 940 b 1/v up to 10 keV
3He(n,p)3H Q 0,764 MeV, Ep 0,573 MeV, EH
0,191 MeV sth 5330 b 1/v up to 2 keV
Reactions used for detection of fast neutrons
threshold reactions
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Induced fission (n,f)
Induced by low energy neutrons (thermal) 233U,
235U, 239Pu
Exothermic with very high Q 200 MeV
Induced by fast neutrons 238U, 237Np, 232Th
Induced by relativistic neutrons 208Pb
High energies E gt 0,1 GeV ? reaction of
protons and neutrons are similar
Spallation reactions, hadron shower
Interaction of realativistic and
ultrarelativistic neutrons
Same behavior as for protons and nuclei