THE EGS5 CODE SYSTEM

Davies, Bethe and Maximon[49] (e.g., see their formula 36, p. 791)) and is given bywheref c (Z) = a 2∞ ∑ν=1a = α Z .1ν(ν 2 + a 2 )(2.52)They also suggest a formula accurate to 4 digits up to a = 2/3 (which corresponds to Uranium);namely,f c (Z) = a 2 { (1 + a 2 ) −1 + 0.20206 − 0.0369a 2 + 0.0083a 4 − 0.002a 6} (2.53)which function FCOULC of PEGS uses to evaluate f c (Z).ξ(Z) is a function which is used to take into account bremsstrahlung and pair productionin the field of the atomic electrons. Strictly speaking, these interactions are different from thecorresponding nuclear interaction not only because the mass and charge of an electron are differentfrom the nuclear mass and charge, but also because of the identity of the electrons. Because of thelightness of the electron, it may be ejected from the atom. In the bremsstrahlung case what wereally have is radiative Møller or Bhabha scattering. In the case of pair production, if the atomicelectron is ejected, we have three rather than two energetic electrons and the reaction is calledtriplet production. Because of the electron exchange effects and the γ − e interactions between theexternal photon and the target electron, and also because the target can no longer be treated asinfinitely heavy, the cross section calculations for these interactions are more complicated than forthe corresponding nuclear cases and involve a larger number of approximations (see p. 631 of Motzet al. [111]). As will be seen below, the ratio of cross sections for the interaction in the electronfields to those in the nuclear field is of the order of 1/Z. Thus, for medium-low to high Z, thecontributions of the atomic electrons are rather minor. On the other hand, for low Z, such asberyllium and certainly for hydrogen, these interactions are very significant and a more accuratetreatment of these interactions is warranted. Nevertheless, we have not treated the bremsstrahlungand pair production in the electronic fields in a special way, primarily because most applicationsof interest do not involve only very low Z elements. When low Z elements are involved, they haveusually been mixed with higher Z elements, in which case the pair production and bremsstrahlungin the low Z elements are relatively unimportant. This does limit somewhat the universality ofEGS.For very high energy incident particles the screening can be considered complete. In thiscase, relatively simple formulas for the interaction in the atomic field can be obtained (Betheand Ashkin[24] (formula 59 on p. 263 and formula 119 on p. 332), Koch and Motz[91] (formulaIII-8 on p. 949)). The relative values of the radiation integralφ rad ≡ 1 E 0∫ kmax0k dσ Bremdkdk (2.54)can be used as an estimate of the relative magnitude of the interactions in the electron or nuclearfields. In the completely screened nuclear field, the radiation integral (formula 4CS of Koch andMotz[91] ) isφ rad,nucleus = 4αr0 2 Z[ln 2 (183 Z −1/3 ) + 1 ]18 − f c(Z) . (2.55)41