Interactions of Ionizing Radiation

Attenuation Collimated beam: Absorber Collimator Beam Intensity I0 x Collimated beam: dI = –N dx N = atomic density  = cross section Integrating gives: I = I0 exp(-N x) = I0 exp(- x)  linear attenuation coefficient – depends on density   m =  / mass-attenuation coefficient

Coefficients Linear attenuation coefficient (, cm-1) Depend on the energy of the photons the nature of the material Mass attenuation coefficient (/, cm2/g) Independent of density of material Depend on the atomic composition

Interactions of photons with matter Photo disintegration (>10 MeV) Coherent scattering (coh) Photoelectric effect () Compton effect (c) Pair production ()

They have very different dependencies on photon energy Eγ and atomic number Z of the absorbing medium.

Coherent scattering Classical scattering or Rayleigh scattering   K L M Classical scattering or Rayleigh scattering No energy is changed into electronic motion No energy is absorbed in the medium The only effect is the scattering of the photon at small angles. In high Z materials and with photons of low energy

Photoelectric effect (1) A photon interacts with an atom and ejects one of the orbital electrons. h-EB

KEpe = Eγ - Ф Ф = electron binding energy Photoelectric effect Incident photon E Photo-electron E -  Complete conversion of Eγ into 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

Secondary effects Vacancy is filled by an electron from a higher shell Leading to: Secondary photon (X-ray fluorescence) or Electron emission (Auger electron) There may be a cascade of secondary emission Depositing all the energy in the medium contributes to a full-energy peak in the spectrum

Photoelectric effect (2) 15 keV L absorption edge /  Z3/E3 The angular distribution of electrons depends on the photon energy. 88 keV K absorption edge

Compton scattering Recoil electron Incident photon Scattered photon h’ Compton scattering

Compton electron Compton effect (1) K L M h   h’ Free electron The photon interacts with an atomic electron as though it were a “free” electron. The law of conservation of energy The law of conservation of momentum …………(1) ………(2) …...…………(3)

Compton effect (2)  = h0/m0c2 = h0/0.511 E h0 h’ By (1), (2), (3) Free electron   h’ By (1), (2), (3)  = h0/m0c2 = h0/0.511

KE(electron) = always < E incident photon Maximum when h’ = min ( = 180o)  Compton edge Minimum (zero) when h’= max at  = 0o

Compton Scattering scattered electron (Ese) incident photon (Eip) loosely bound electron (Eie) scattered electron (Ese) incident photon (Eip)   scattered photon (Esp)

Compton Scattering Ese = mc2 Eie = moc2 Eip = hc ip E*sp = hc sp hc   Ese = mc2 Eie = moc2 Eip = hc ip E*sp = hc sp hc ip + moc2 = sp + mc2 Conservation of Energy:

Compton Scattering Pse = mv Pie = 0 Pip = h ip P*sp = h sp   P*sp = h sp Conservation of Momentum: h ip = sp cos + mv cos horizontal vertical 0 = h sp sin + mv sin

Special cases of Compton effect The radiation scattered at right angles (=90°) is independent of incident energy and has a maximum value of 0.511 MeV. The radiation scattered backwards is independent of incident energy and has a maximum energy of 0.255 MeV.

Dependence of Compton effect on energy As the photon energy increase, the photoelectric effect decreases rapidly and Compton effect becomes more and more important. The Compton effect also decreases with increasing photon energy.

Dependence of Compton effect on Z Independent of Z Dependence only on the number of electrons per gram electrons/g

Pair production  KE(pair) = E - 2mc2 - deposited in medium h’= 511 keV Positron h’= 511 keV  Incident photon E Electron KE(pair) = E - 2mc2 - deposited in medium Pair production can only occur near a heavy body (atom) Positron (anti-electron) slows down then attracts and annihilates with an electron. Two (511 keV) photons are created – emitted back-to-back

The photon interacts with the electromagnetic field of an atomic nucleus. The threshold energy is 1.02 MeV. The total kinetic energy for the electron-positron pair is (h-1.02) MeV - deposited in medium

Relative importance of -ray interactions