Calorimeters Chapter 3 Chapter 3 Interactions of Photons

Calorimeters Chapter 3 Overview on Photon Absorption Cross Section General: Beer’s Absorption Law: I= I 0 e -  x,  = Absorptioncoefficient l From: E  [MeV]  Phot.  Coh.  incoh.  Pair Nuc.  Pair Elek. Photonabsorption Cross Section in Pb barns/atom Different Processes for different Energies: 1) Photoelectric Effect E ≤ 500 keV 2) Compton Scattering 500 keV < E < 5 MeV 3) Pair Production E > 2m e

Calorimeters Chapter 3 Photoelectric Effect Incident photon E  Photo-electron E  -  Complete conversion of E γ 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 KE pe = E γ - Ф Ф = electron binding energy

Calorimeters Chapter 3 Photoeffect:  Phot.  +Atom  Atom + + e - I 0 << E  << m e c 2 a B = Bohr radius, r e = class. Electronradius Photoelectric effect - Outline of Derivation (for full derivation see end of lecture) Shell electron couples to free electromagnetic wave Electromagnetic field is perturbation to atomic system Typical derivation assumes scattering on K-Shell electrons  Z dependence of cross-section Assumption on energy of released electron allows for Born approximation. ‘Text book’ formula:

Calorimeters Chapter 3 Compton scattering Incident photon E  Recoil electron Scattered photon E   E = E  - E  = E – mc 2   p γ = E  /c p  = E  /c  p Conservation of momentum and energy (p) 2 = (p γ ) 2 + (p  ) p γ p  cos θ (pc) 2 = (E γ ) 2 + (E  ) 2 - 2E γ E  cos θ = E 2 – m 2 c 4 And E  - E  = E – mc 2

Calorimeters Chapter 3 Energy of Scattered  Eliminating E gives:  E(electron) = E  - E  always < E  Maximum when E  = min (  = 180 o )  Compton edge Minimum (zero) when E  = max (= E  ) at  = 0 o

Calorimeters Chapter 3 Schematic View on Compton Spectrum If scattered γ-ray escapes:  Continuum, called Compton plateau Compton edge E EγEγ 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) 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~ Z 5 ‘Possibility of Compton Scattering increases with Z - Weaker energy dependency than photoeffect Compton Scattering dominates above ~500 keV

Calorimeters Chapter 3 Pair Production Process From Kinematics: e+e+ e-e- Threshold Energy 1.2 MeV Energy Spectrum of e + e - With increasing energy pair production becomes rapidly dominant source of energy deposition by photons Pair Production can only occur Near heavy body (atom)

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?