1. Gamma ray interaction with matter A) Primary interactions 1) Coherent scattering (Rayleigh scattering) 2) Incoherent scattering (Compton scattering) 3) Photoelectric effect 4) Production of electron and positron pairs 5) Interactions with small contributions 6) Total attenuation of gamma rays at matter B) Secondary interactions 1) X-rays 2) Auger electrons 3) Annihilation of positron and electron 4) Bremsstrahlung radiation γ e-e- e-e- γ e-e- γ e+e+ e-e- γ

2. Coherent scattering Coherent scattering on bounded electrons (whole atom) (energy is not transfered only direction of momentum is changed) – in the limit Rayleigh scattering Thomson scattering – scattering on free electrons in classical limit (coherent as well as incoherent) Polar graph of cross-section without inclusion of F(q,Z) influence, classical limit of Thomson scattering F(q,Z) – probability of momentum transfer on Z electron atom without energy transfer High energy → scattering to small angles r 0 – classical electron radius (SI units): Unpolarized: Polarized: E γ, ν E γ `, ν´ Θ E γ = E γ ´,ν = ν´ α = 1/137 ħc = 197 MeV  fm m e c 2 = 0,511 MeV

3. Diffraction on crystal lattice Usage of interference during coherent scattering on layers of crystal lattice Bragg law: n·λ = 2d·sin Θ d – grid spacing λ – radiation wave length n – diffraction order E γ [keV] 1 10 50 100 500 1000 2000 ν [EHz = 10 18 Hz] 0,242 2,42 12,1 24,2 121 242 484 λ [nm] 1,24 0,124 0,025 0,0124 0,0025 0,00124 0,00062 Grid spacing is in the order of 0,1 – 1 nm Dependency of first diffraction maximum angle on X-ray and gamma ray energies for two grid spacings Spectrometers with sizes up to ten meters were built: E γ = 1000 keV, d = 0,6 nm, r = 10 m → Θ = 0,059 O, x = 10 mm E γ = 100 keV → Θ = 0,59 O, x = 100 mm

4. Incoherent (Compton scattering) Where parameter: Relation between scattered photon energy E γ and scattering angle Θ We obtain relations between energies and angles of scattering and reflection from the energy and momentum conservation laws We assumed: 1) scattering on free electron (E γ >>B e ) 2) electron is in the rest Θ φ E γ, p γ =E γ /c E γ ’, p γ ’=E γ ’/c m e c 2, p e = 0 Scattered photon energy: Reflected electron energy: Reflection angle:

5. Polar graph of cross-section without inclusion of S(q,Z) influence. In the limit E → 0 we obtain graph for coherent scattering Diferential cross-section is described by Klein-Nishin equation (on free electrons): We introduce energy of scattered photon: inclusion of influence of electron binding at atom → multiplying by function S(q,Z) – probability of momentum q transfer to electron during ionization or excitation Total cross section (can be obtained by integration): Distribution of energy transferred to electrons E γ > m e c 2 → ζ > 1 : Scattering of high energy electron and low energy photon – inverse Compton scattering (see exercise)

6. Photoelectric effect Can pass only on bounded electron Total photon energy is transfered Electron energy: E e = E γ - B e and so σ F = ~ Z 5 ·E γ -3,5 near to K-shell σ F = ~ Z 4,5 ·E γ -3 Cross-section (for E γ << m e c 2 ): Accurate calculation of photoeffect process (solution of Dirac equation) is very sophisticated: γ e-e- If it is enough energy (E γ > B eK binding energy on K-shell) the photoeffect will pass almost only on these electrons whereis fine structure constant More accurate equation for σ F near to K-shell see Leo Dependency of K-shell electron binding energy on proton number Z of atom (Si – 1,8389 keV, Ge – 11.1031 keV, Pb – 88.0045 keV)

7. Production of electron and positron pairs e+e+ e-e- γ σ P ~ Z 2 ln(2E γ ) Transformation of photon to electron and positron pair. Energy and momentum conservation laws → only In nucleus field (mostly) E γ > 2m e c 2 = 1022 keV eventually electrons E γ > 4m e c 2 = 2044 keV (je 1-2  Z smaller) where f(Z) is coulomb correction of order α 2 Dependency of σ P on Z and E γ is: (for „lower energies“ range) There is valid for cross-section in special cases: Without screening: Complete screening: Production in the electron field („triplet“ production) E γ >>m e c 2 electrons and positrons are peaked forward Θ ≈ 1/ζ Cross-section dependency On photon energy Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence: predominance of pair production near nucleus – without screening):

8. Interaction with small contribution Photonuclear reactions – resonance processes with small probability Photon interaction with coulomb field of nucleus (Delbrück scattering) – we can look on it as on virtual pair production and following annihilation Photonuclear reactions in order of mbarn up to barn in narrow energy range interaction with electrons in order of barns up to 10 5 barns in broad energy range Nuclear Rayleigh scattering Nuclear Thomson scattering – substitutions e →Ze, m e → M j and then Nuclear resonance scattering ( for example giant dipole resonance) Total cross-sections:

9. X-ray Auger electrons proton záření gamaelektron Fluorescent efficiency (coefficient): Bremsstrahlung radiation during movement of electrons and positrons N X – X-ray photons N A – Auger electrons Released energy is transferred during electron transition at atomic cloud on other electron Passage of electrons and positrons: 1)Ionization losses 2)Bremsstrahlung radiation Charged particle moves in nuclear field with acceleration → it emits photons Annihilation of positron and electron Positrons are stopped by ionization losses and they annihilate in the rest → 2 quanta of 511 keV (they are not fully in the rest → energy smearing of annihilation quanta) Secondary processes

10. Total absorption of gamma rays at matters Review of main processes σ = σ F + σ C + σ P Total cross-sections: Multiply by number of atoms per volume unit N: where N a – Avogadro constant, A – atomic mass, ρ – material density μ – total absorption coefficient – inverse value of mean free path of photon at material Photon can loss big part (even all) its energy in one interaction → beam weakens, it has not fixed range Equation for decreasing of photon number: For compound or mixture Bragg rule is valid: Total cross-section dI = -μ  I  dx