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Method

Let's call dσ(Z,T,k)/dk the differential cross-section for production of a photon of energy k by an electron of kinetic energy T in the field of an atom of charge Z, and kc the energy cut-off below which the soft photons are treated as continuous energy loss ( BCUTE in the program). Then the mean value of the energy lost by the electron due to soft photons is ELossbrem(Z,T,kc) = ∫0kck{d σ(Z,T,k)dk}dk

whereas the total cross-section for the emission of a photon of energy larger than kc is σbrem(Z,T,kc) = ∫kcT{d σ(Z,T,k)dk}dk

Many theories of the bremsstrahlung process exist, each with its own limitations and regions of applicability. Perhaps the best synthesis of these theories can be found in the paper of S.M. Seltzer and M.J. Berger []. The authors give a tabulation of the bremsstrahlung cross-section dσ/dk differential in the photon energy k, for electrons with kinetic energies T from 1 keV to 10 GeV. For electron energies above 10 GeV the screened Bethe-Heitler differential cross-section can be used [,] together with the Midgal corrections [,]. The first of the two Migdal corrections is important for very high electron energies only (T ≥ 1 TeV) and has the effect of reducing the cross-section. The second Migdal correction is effective even at ``ordinary'' energies (100 MeV -- 1 GeV) and it decreases the differential cross-section at photon energies below a certain fraction of the incident electron energy (dσ/dk decreases significantly if k/T ≤10-4 .)



Janne Saarela
Mon Apr 3 12:46:29 METDST 1995