THE EGS5 CODE SYSTEM

Figure 2.2: Feynman diagrams for bremsstrahlung and pair production.2.7 Bremsstrahlung and Electron-Positron Pair ProductionThe bremsstrahlung and pair production processes are closely related, as can be seen from theFeynman diagrams in Figure 2.2 . In the case of bremsstrahlung, an electron or positron is scatteredby two photons: a virtual photon from the atomic nucleus and another free photon which is createdby the process. In the case of pair production, an electron traveling backward in time (a positron)is also scattered by two photons, one of which scatters it forward in time making it into an electron.The net effect is the absorption of the photon and creation of an electron-positron pair.The discussions and descriptions of these processes which are given here use formulas taken fromthe review articles by Koch and Motz[91] on bremsstrahlung and by Motz, Olsen and Koch[111]on pair production. We also employ some ideas from Butcher and Messel[39] for mixing the crosssections for sampling of the secondary spectra. Below 50 MeV the Born approximation crosssections are used with empirical corrections added to get agreement with experiment. Above 50MeV the extreme relativistic Coulomb corrected cross sections are used.The “shower book” by Messel and Crawford[103] takes into account the Landau-Pomeranchuk-Migdal (LPM) “suppression effect”[95, 94, 106] which is important at electron energies greaterthan 100 GeV for bremsstrahlung and greater than a TeV or so for pair production. At theseenergies, the LPM effect, which had been demonstrated experimentally [9], manifests as significantreductions (“suppression”) in the total bremsstrahlung and pair production cross sections. EGS5does not currently model the LPM effect. In addition, an effect due to polarization of the medium(which apparently is effective even at ordinary energies) results in the cutoff of the bremsstrahlungdifferential cross section at secondary photon energies below a certain fraction of the incidentelectron energy. This has been quantified in terms of a factor F P [103], given byF P =(1 + nr 0λ 2 0 E2 0πk 2 ) −1(2.37)where n is the electron density, r 0 is the classical electron radius, λ 0 is the Compton wavelength ofan electron, and E 0 and k are the energies of the electron and photon, respectively. If we define acutoff energy byk c = E 0√nr 0 λ 2 0 /π (2.38)37