1. 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 Mostly neutron loses only part of energy Important cross sections of nuclear interactions

2. 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 < 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 20 o C 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 < 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 > 10 GeV

3. 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 The heavier nucleus the lower energy can neutron transferred to it: Maximal transferred energy (nonrelativistic case of head-head collision): MCL: p n0 = p A - p n ECL: E n0KIN = E AKIN + E nKIN  p n0 2 /2m n = p A 2 /2m A + p n 2 /2m n MCL: p n 2 = p A 2 – 2p A p n0 + p n0 2  m A p n 2 = m A p A 2 – 2m A p A p n0 + m A p n0 2 ECL: m A p n 2 = - m n p A 2 + m A p n0 2 We subtract equation: 0 = m A p A 2 + m n p A 2 – 2m A p A p n0  m A p A + m n p A = 2m A p n0 Nucleon number A

4. p n = p n0 ·cosθ  E n = E n0 ·cos 2 θp p = p n0 ·sinθ  E p = E n0 ·sin 2 θ Usage of hydrogen (θ – neutron scattering angle, ψ – proton reflection angle) m p = m n : p p = p n0 ·cosψ  E p = E n0 ·cos 2 ψ p n = p n0 ·sinψ  E n = E n0 ·sin 2 ψ ψ = π/2-θ Dependency of energy transferred to proton on reflected angle For nucleus: Elastic scattering: in our case particle 1 – neutron particle 2 – proton, generally nucleus Reflection angle φ

5. Equation can be rewrite to: For elastic scattering is valid: Ratio of these relations leads to: 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: Laboratory coordinate system Centre of mass coordinate system and then and required relation is valid: Small expose with derivation of relation between laboratory and centre of mass angles: derive! Insertion

6. σ S (θ CM ) - isotropy  σ S (θ CM ) = σ S /(4π) (it is valid approximately for protons up to E n0 < 10 MeV) Energy distribution of reflected protons for E n0 < 10 MeV Efficiency ε is given: We determine appropriate differential dE A : 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: Introduce for dE A :

7. Diffraction of neutrons on crystal lattice is used E [eV]0,0010,0050,010,11101001000 λ [nm]0,910,410,290,0910,0290,00910,00290,00091 Lattice constants are in the order 0,1 – 1 nm → Neutron energy in the orders of meV up to eV Mentioning: Bragg law: n·λ = 2d·sin Θ E n << m n c 2 = 0,0288 eV ½ ∙nm for E n in [eV] Coherent scattering – diffraction on lattice Magnitude of energy neither momentum and wave length of neutrons are not changed

8. Nuclear reactions of neutrons Neutron capture: (n,γ) Cross section of reaction 139 La(n,γ) 140 La Resonance regionThermal region High values of cross sections for low energy neutrons Exothermic reactions 157 Gd(n,γ) – for thermal neutrons cross section is biggest σ ~ 255 000 barn Released energy allows detection Inelastic neutron scattering Part of energy is transformed to excitation → accuracy of energy determination is given by their fate Competitive process to elastic scattering on nuclei heavier than proton Its proportion increases with increasing energy

9. Reaction (n, 2n), (n,3n),...Endothermic (threshold) reactions Reactions (n,d), (n,t), (n,α)... Reactions used for detection of low energy neutrons (exoenergy): 10 B(n,α) 7 Li Q = 2,792 and 2,310 MeV, E α = MeV, E Li = MeV σ th = 3840 b 1/v up to 1 keV 6 Li(n,α) 3 H Q = 4,78 MeV, E α = 2,05 MeV, E H = 2,73 MeV σ th = 940 b 1/v up to 10 keV 3 He(n,p) 3 H Q = 0,764 MeV, E p = 0,573 MeV, E H = 0,191 MeV σ th = 5330 b 1/v up to 2 keV E N + E P = Q m N v N = m P v P → (two particle decay of compound nucleus at rest, nonrelativistic approximation) Examples of threshold reactions: 197 Au(n,2n) 196 Au 197 Au(n,4n) 194 Au 27 Al(n,α) 24 Na Reactions used for detection of fast neutrons – threshold reactions Threshold reactions Bi(n,Xn)Bi Energy [MeV] Cross section [barn] Energy [MeV] Cross section [barn]

10. Induced fission: (n,f) Exothermic with very high Q ~ 200 MeV Induced by low energy neutrons (thermal): 233 U, 235 U, 239 Pu Induced by fast neutrons: 238 U, 237 Np, 232 Th Induced by „relativistic“ neutrons: 208 Pb High energies E > 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 Cross section [rel.u]