Chapter 5 Interactions of Ionizing Radiation

Ionization The process by which a neutral atom acquires a positive or a negative charge Directly ionizing radiation – electrons, protons, and  particles –sufficient kinetic energy to produce ionization  ray excitation Indirectly ionizing radiation – neutrons and photons –to release directly ionizing particles from matter when they interact with matter

Photon beam description Fluence (  ) Fluence rate or flux density (  ) Energy fluence (  ) Energy fluence rate, energy flux density, or intensity (  )

Photon beam attenuation x–the absorber thickness (cm)  –linear attenuation coefficient (cm -1 ) I–intensity

Half-value layer (HVL) x=HVL I/I 0 =1/2 A mono-energetic beam A practical beam produced by an x-ray generator

Coefficients (1) Linear attenuation coefficient ( , cm -1 ) –Depend on the energy of the photons the nature of the material Mass attenuation coefficient (  / , cm 2 /g) –Independent of density of material –Depend on the atomic composition

Coefficients (2) Electronic attenuation coefficient ( e , cm 2 /electron) Atomic attenuation coefficient ( a , cm 2 /atom) Z the atomic number N 0 the number of electrons per gram N A Avogradro’s number A W the atomic weight

Coefficients (3) Energy transfer coefficient (  tr ) –When a photon interacts with the electrons in the material, a part or all of its energy is converted into kinetic energy of charged particles. The average energy transferred into kinetic energy of charged particles per interaction

Coefficients (4) Energy absorption coefficient (  en ) –Energy loss of electrons Inelastic collisions losses  ionization and excitation Radiation losses  bremsstrahlung –  en =  tr (1-g) –g fraction energy loss to bremsstrahlung increses with Z of the absorber the kinetic energies of the secondary particles

E tr = ? E en =? 1 MeV (Initial Energy of Compton Electron, E e ) (Bremsstrahlung) (Scattered Photon) 0.3 MeV 0.7 MeV 0.2 MeV (Incident Photon, h ) Energy imparted of photon

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

Coherent scattering 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 K L M

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

Photoelectric effect (2)  /   Z 3 /E 3 The angular distribution of electrons depends on the photon energy.  15 keV L absorption edge  88 keV K absorption edge

Compton effect (1) 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 K L M h   h ’ Free electron Compton electron …………(1) ………(2) …...…………(3)

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

Special cases of Compton effect The radiation scattered at right angles (  =90°) is independent of incident energy and has a maximum value of MeV. The radiation scattered backwards is independent of incident energy and has a maximum energy of 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 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. h E-E- E+E MeV Positron annihilation

The probability of pair production   Z 2 /atom

PE effect Compton effect PP production h h h EeEe E+E+ E-E- The relationships between  and  tr

PE effect Compton effect PP production h h h EeEe E+E+ E-E- The relationships between  tr and  en

The comparison between  and  en

Interactions of charged particles Coulomb force –Collisions between the particle and the atomic electrons result in ionization and excitation. –Collisions between the particle and the nucleus result in radiative loss of energy or bremsstrahlung. Nuclear reactions Stopping power (S) = Mass stopping power (S/ , MeV cm 2 /g)

Heavy charged particles The particle slows down  energy loss   ionization or absorbed dose  Bragg peak

Electrons Multiple changes in direction during the slowing down process smears out the Bragg peak. Ionization Excitation Bremsstrahlung

Interactions of neutrons Recoiling protons from hydrogen and recoiling heavy nuclei from other elements –A billiard-ball collision –The most efficient absorbers of a neutron beam are the hydrogenous materials. Nuclear disintegrations –The emission of heavy charged particles, neutrons,and  rays –About 30% of the tissue dose

Comparative beam characteristics (1) Neutron beams

Comparative beam characteristics (2) Heavy charged particle beams

Comparative beam characteristics (3) Electron beams & protons

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