THE EGS5 CODE SYSTEM

where δ = 272 Z −1/3 ∆ as before, and where F (q, Z) is the atomic form factor for an atom withatomic number Z. Following Nagel[112], we have used the Thomas-Fermi form factors, for whichφ 1 and φ 2 are Z independent and have already been evaluated. Butcher and Messel [39]haveapproximated the screening functions to within 1–2% by the formulasandφ 1 (δ) = (20.867 − 3.242δ + 0.625δ 2 if δ ≤ 1, 21.12 − 4.184 ln(δ + 0.952)) (2.50)φ 2 (δ) = (20.029 − 1.930δ − 0.086δ 2 if δ ≤ 1, 21.12 − 4.184 ln(δ + 0.952)). (2.51)The Thomas-Fermi screening is quite accurate for high atomic numbers, but at low atomic numbersits accuracy decreases. The Hartree form factors are better for low Z. Tsai[172] has given a reviewof bremsstrahlung and pair production cross sections including best estimates of form factors andscreening functions, and Seltzer and Berger[153, 154] have reviewed and presented new cross sectiondata for bremsstrahlung production. EGS has not been modified to reflect these more accurate crosssections except that it redefines the radiation length and ξ i to be consistent with the definitionsby Tsai[172] (see discussion of these changes below). We have also checked that, for example, thevalues of φ 1 and φ 2 , given by Equations 2.50 and 2.51, agree with Tsai’s values within 0.4% forZ > 4 and within 5% for hydrogen.A ′ (Z, Ĕ0) in Equation 2.43 is an empirical correction factor evaluated by the function APRIMin PEGS. For Ĕ 0 > 50 MeV, PEGS takes A ′ = 1 since it uses the Coulomb corrected formulas ,which are accurate to about 3% in this energy range. For Ĕ0 < 50 MeV, PEGS5 uses values of A ′generated by Rogers et al. [139]. This effectively renormalizes the bremsstrahlung cross sectionsto assure that the total radiative stopping powers (see section 2.13) agree with those publishedin ICRU Report 37 [79]. As an option, the user may request the PEGS4 corrections, which wereinterpolated in Z from the curves of Koch and Motz[91] (see their Figure 23, e.g.). With theavailability of the better cross section data mentioned above, this methodology is somewhat moreapproximate than need be, and an improved treatment awaits development by some fresh, energeticEGS5 user.The pair production empirical correction factor A ′ p(Z, ˘k) in Equation 2.44 is defined as: A ′ p(Z, ˘k)is equal to (“The Best Empirical Estimate of the Total Pair Production Cross Section for givenZ, ˘k”) divided by (“The Total Pair Production Cross Section obtained by integrating Equation 2.44over all allowed Ĕ+ values, with A ′ p = 1”). For ˘k < 50 MeV, we take this best estimate to be thedata compiled by Storm and Israel[167] and in fact we use this data directly without resorting toEquation 2.44 whenever pair production total cross sections are needed for ˘k < 50. For ˘k > 50MeV, an integration of Equation 2.44 with A ′ p = 1 is used for the pair production total cross section.This agrees within a few percent with Storm and Israel[167] up to the limiting energy for which theypresent data but it does lead to a slight discontinuity in the photon cross section at 50 MeV. ThusA ′ p(Z, ˘k > 50) is taken to be 1, as it is for bremsstrahlung. Unlike as with bremsstrahlung, however,A ′ p is never explicitly calculated since it is not needed in determining the total cross section, nor,as will be seen later, is it used in sampling the secondary particle energies.The f c (Z) in Equations 2.43 and 2.44 is the Coulomb correction term that was derived by40