THE EGS5 CODE SYSTEM

Figure 2.2: Feynman diagrams for bremsstrahlung and pair production.
2.7 Bremsstrahlung and Electron-Positron Pair Production
The bremsstrahlung and pair production processes are closely related, as can be seen from the
Feynman diagrams in Figure 2.2 . In the case of bremsstrahlung, an electron or positron is scattered
by two photons: a virtual photon from the atomic nucleus and another free photon which is created
by 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 from
the 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 cross
sections for sampling of the secondary spectra. Below 50 MeV the Born approximation cross
sections are used with empirical corrections added to get agreement with experiment. Above 50
MeV 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 greater
than 100 GeV for bremsstrahlung and greater than a TeV or so for pair production. At these
energies, the LPM effect, which had been demonstrated experimentally [9], manifests as significant
reductions (“suppression”) in the total bremsstrahlung and pair production cross sections. EGS5
does 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 bremsstrahlung
differential cross section at secondary photon energies below a certain fraction of the incident
electron energy. This has been quantified in terms of a factor F P [103], given by
F P =
(
1 + nr 0λ 2 0 E2 0
πk 2 ) −1
(2.37)
where n is the electron density, r 0 is the classical electron radius, λ 0 is the Compton wavelength of
an electron, and E 0 and k are the energies of the electron and photon, respectively. If we define a
cutoff energy by
k c = E 0
√nr 0 λ 2 0 /π (2.38)
37