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 with
atomic number Z. Following Nagel[112], we have used the Thomas-Fermi form factors, for which
φ 1 and φ 2 are Z independent and have already been evaluated. Butcher and Messel [39]have
approximated the screening functions to within 1–2% by the formulas
and
φ 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 numbers
its accuracy decreases. The Hartree form factors are better for low Z. Tsai[172] has given a review
of bremsstrahlung and pair production cross sections including best estimates of form factors and
screening functions, and Seltzer and Berger[153, 154] have reviewed and presented new cross section
data for bremsstrahlung production. EGS has not been modified to reflect these more accurate cross
sections except that it redefines the radiation length and ξ i to be consistent with the definitions
by Tsai[172] (see discussion of these changes below). We have also checked that, for example, the
values of φ 1 and φ 2 , given by Equations 2.50 and 2.51, agree with Tsai’s values within 0.4% for
Z > 4 and within 5% for hydrogen.
A ′ (Z, Ĕ0) in Equation 2.43 is an empirical correction factor evaluated by the function APRIM
in 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 sections
to assure that the total radiative stopping powers (see section 2.13) agree with those published
in ICRU Report 37 [79]. As an option, the user may request the PEGS4 corrections, which were
interpolated in Z from the curves of Koch and Motz[91] (see their Figure 23, e.g.). With the
availability of the better cross section data mentioned above, this methodology is somewhat more
approximate than need be, and an improved treatment awaits development by some fresh, energetic
EGS5 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 given
Z, ˘k”) divided by (“The Total Pair Production Cross Section obtained by integrating Equation 2.44
over all allowed Ĕ+ values, with A ′ p = 1”). For ˘k < 50 MeV, we take this best estimate to be the
data compiled by Storm and Israel[167] and in fact we use this data directly without resorting to
Equation 2.44 whenever pair production total cross sections are needed for ˘k < 50. For ˘k > 50
MeV, 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 they
present data but it does lead to a slight discontinuity in the photon cross section at 50 MeV. Thus
A ′ 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 by
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