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Chapter 3 Interactions of Photons Calorimeters Chapter 3 Overview on Photon Absorption Cross Section barns/atom General: Beer’s Absorption Law: I= I0e-x, = Absorptioncoefficientl Different Processes for different Energies: Photonabsorption Cross Section in Pb 1) Photoelectric Effect E ≤ 500 keV 2) Compton Scattering 500 keV < E < 5 MeV 3) Pair Production E > 2me Phot. incoh. Coh. Pair Nuc. Pair Elek. From: http://www.nist.gov E[MeV] Calorimeters Chapter 3 Photoelectric Effect Incident photon E Photo-electron E - Complete conversion of Eγ releasing an atomic electron - usually from an inner atomic shell • Occurs near an atom to conserve energy and momentum • The photoelectron is ejected with kinetic energy KEpe = Eγ - Ф Ф = electron binding energy Calorimeters Chapter 3 Photoelectric effect - Outline of Derivation (for full derivation see end of lecture) Photoeffect: Phot. +Atom Atom+ + eI0 << E<< mec2 aB = Bohr radius, re = class. Electronradius Shell electron couples to free electromagnetic wave Electromagnetic field is perturbation to atomic system Typical derivation assumes scattering on K-Shell electrons 3/2 Zr 1 Z exp aB aB Z dependence of cross-section Assumption on energy of released electron allows for Born approximation. ‘Text book’ formula: 7 I 2 0 Phot. aB2 Z 5 E Calorimeters Chapter 3 Compton scattering Incident photon E Recoil electron E = E - E = E – mc2 Scattered photon E pγ = E /c p p = E /c Conservation of momentum and energy (p)2 = (pγ)2 + (p )2 - 2 pγ p cos θ (pc)2 = (Eγ)2 + (E )2 - 2Eγ E cos θ = E2 – m2c4 And E - E = E – mc2 Calorimeters Chapter 3 Energy of Scattered Eliminating E gives: E ' E 1 ( E / mc )(1 cos ) 2 E(electron) = E - E always < E • Maximum when E = min ( = 180o) Compton edge • Minimum (zero) when E = max (= E) at = 0o Calorimeters Chapter 3 Schematic View on Compton Spectrum If scattered γ-ray escapes: Continuum, called Compton plateau Compton edge Full-energy peak Eγ E • γ-ray may scatter more than once, with more energy E deposited each time • If scattered γ-ray undergoes photo-electric effect all energy is deposited (full-energy peak) Calorimeters Chapter 3 Z dependency of Compton Scattering - Only weak Z dependency of Cross Section ~Z Compare with strong dependency of photoeffect~ Z5 ‘Possibility of Compton Scattering increases with Z - Weaker energy dependency than photoeffect Compton Scattering dominates above ~500 keV Calorimeters Chapter 3 Pair Production Process e+ Energy Spectrum of e+ee- From Kinematics: EMin. 2mec 2 Threshold Energy 1.2 MeV Pair Production can only occur Near heavy body (atom) With increasing energy pair production becomes rapidly dominant source of energy deposition by photons Calorimeters Chapter 3 Discussion of Photon Interactions I Relative importance of -ray interactions Calorimeters Chapter 3 Discussion of Photon Interactions II Being in the experimental Pit - Shielding against rays What is the most difficult to shield ? a) 1-500 keV X-Rays b) Few MeV rays c) Several MeV rays (up to ~100 MeV) Which effect dominates in which energy domain? Calorimeters Chapter 3