Neutron interaction with matter

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

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 Coldand 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 neutronsandresonance neutrons: E = (0,5 eV – 1000 eV) Cadmium threshold: ~ 0,5 eV- with higher energy pass through 1 mm of Cd Slow neutrons: E < 1keV Neutrons with middle energies: E = (1keV – 500keV) Fast neutrons: E = (0,5MeV – 20 MeV) Neutrons with high energies: E = (20 MeV – 100 MeV) Relativistic neutrons: 0,1 – 10 GeV Ultrarelativistic neutrons: E > 10 GeV

3. Nucleon number A 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 reflectedduring 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 transferredto it:

4. Reflection angle φ Usage of hydrogen (θ – neutron scattering angle, ψ – proton reflection angle) mp = mn: pn = pn0·cosθEn = En0·cos2θ pp = pn0·sinθ Ep = En0·sin2θ ψ = π/2-θ pp = pn0·cosψ Ep = En0·cos2ψ pn = pn0·sinψ En = En0·sin2ψ For nucleus: Elastic scattering: in our case particle 1 – neutron particle 2 – proton, generally nucleus Dependency of energy transferred to proton on reflected angle

5. 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:

6. σS(θCM) - isotropy  σS(θCM) = σS/(4π) 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 < 10 MeV) Energy distribution of reflected protons for En0 < 10 MeV Efficiency εis given:

7. En<<mnc2 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·λ = 2d·sin Θ = 0,0288 eV½∙nm for Enin [eV] Lattice constants are in the order 0,1 – 1 nm→ Neutron energy in the orders of meV up to eV

8. Thermal region Resonance region 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,γ) High values of cross sections for low energy neutrons Exothermic reactions Released energy allows detection Cross section of reaction 139La(n,γ)140La 157Gd(n,γ) – for thermal neutrons cross section is biggest σ ~ 255 000 barn

9. Cross section [barn] Cross section [barn] Energy [MeV] EN + EP = Q mNvN = mPvP→ Energy [MeV] 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,α)24Na Reactions (n,d), (n,t), (n,α) ... Reactions used for detection of low energy neutrons (exoenergy): (two particle decay of compound nucleus at rest, nonrelativistic approximation) 10B(n,α)7LiQ = 2,792 and 2,310 MeV, Eα = MeV, ELi = MeV σth = 3840 b 1/v up to 1 keV 6Li(n,α)3H Q = 4,78 MeV, Eα = 2,05 MeV, EH = 2,73 MeV σth = 940 b 1/v up to 10 keV 3He(n,p)3HQ = 0,764 MeV, Ep = 0,573 MeV, EH = 0,191 MeV σth = 5330 b 1/v up to 2 keV Reactions used for detection of fast neutrons – threshold reactions

10. Cross section [rel.u] Induced fission: (n,f) Induced by lowenergy 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 > 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