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Neutron interaction with matter

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Presentation on theme: "Neutron interaction with matter"— Presentation transcript:

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 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 = (0,5 eV – 1000 eV) Cadmium threshold: ~ 0,5 eV - with higher energy pass through 1 mm of Cd Slow neutrons: E < 1 keV Neutrons with middle energies: E = (1 keV – 500 keV) Fast neutrons: E = (0,5 MeV – 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 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 = - mnpA mApn02 We subtract equation: 0 = mApA2 + mnpA2 – 2mApApn0  mApA + mnpA = 2mApn0 Nucleon number A The heavier nucleus the lower energy can neutron transferred to it:

4 pn = pn0·cosθ  En = En0·cos2θ pp = pn0·sinθ  Ep = En0·sin2θ
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: Reflection angle φ 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:
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 Relation between angular distribution and energy distribution:
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: σS(θCM) - isotropy  σS(θCM) = σS/(4π) (it is valid approximately for protons up to En0 < 10 MeV) Energy distribution of reflected protons for En0 < 10 MeV Efficiency ε is given:

7 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 En << mnc2 = 0,0288 eV½∙nm 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 λ [nm] 0,91 0,41 0,29 0,091 0,029 0,0091 0,0029 0,00091

8 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 Resonance region Thermal region 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 ~ barn

9 Endothermic (threshold) reactions
Reaction (n, 2n), (n,3n), ... Endothermic (threshold) reactions Energy [MeV] Cross section [barn] Threshold reactions Bi(n,Xn)Bi Energy [MeV] Cross section [barn] 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) EN + EP = Q mNvN = mPvP → 10B(n,α)7Li Q = 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)3H Q = 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 Spallation reactions, hadron shower
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 > 0,1 GeV → reaction of protons and neutrons are similar Cross section [rel.u] Spallation reactions, hadron shower Interaction of realativistic and ultrarelativistic neutrons Same behavior as for protons and nuclei


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