THE EGS5 CODE SYSTEM

Davies, Bethe and Maximon[49] (e.g., see their formula 36, p. 791)) and is given by
where
f c (Z) = a 2
∞ ∑
ν=1
a = α Z .
1
ν(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 production
in the field of the atomic electrons. Strictly speaking, these interactions are different from the
corresponding nuclear interaction not only because the mass and charge of an electron are different
from the nuclear mass and charge, but also because of the identity of the electrons. Because of the
lightness of the electron, it may be ejected from the atom. In the bremsstrahlung case what we
really have is radiative Møller or Bhabha scattering. In the case of pair production, if the atomic
electron is ejected, we have three rather than two energetic electrons and the reaction is called
triplet production. Because of the electron exchange effects and the γ − e interactions between the
external photon and the target electron, and also because the target can no longer be treated as
infinitely heavy, the cross section calculations for these interactions are more complicated than for
the corresponding nuclear cases and involve a larger number of approximations (see p. 631 of Motz
et al. [111]). As will be seen below, the ratio of cross sections for the interaction in the electron
fields to those in the nuclear field is of the order of 1/Z. Thus, for medium-low to high Z, the
contributions of the atomic electrons are rather minor. On the other hand, for low Z, such as
beryllium and certainly for hydrogen, these interactions are very significant and a more accurate
treatment of these interactions is warranted. Nevertheless, we have not treated the bremsstrahlung
and pair production in the electronic fields in a special way, primarily because most applications
of interest do not involve only very low Z elements. When low Z elements are involved, they have
usually been mixed with higher Z elements, in which case the pair production and bremsstrahlung
in the low Z elements are relatively unimportant. This does limit somewhat the universality of
EGS.
For very high energy incident particles the screening can be considered complete. In this
case, relatively simple formulas for the interaction in the atomic field can be obtained (Bethe
and Ashkin[24] (formula 59 on p. 263 and formula 119 on p. 332), Koch and Motz[91] (formula
III-8 on p. 949)). The relative values of the radiation integral
φ rad ≡ 1 E 0
∫ kmax
0
k dσ Brem
dk
dk (2.54)
can be used as an estimate of the relative magnitude of the interactions in the electron or nuclear
fields. In the completely screened nuclear field, the radiation integral (formula 4CS of Koch and
Motz[91] ) is
φ rad,nucleus = 4αr0 2 Z
[ln 2 (183 Z −1/3 ) + 1 ]
18 − f c(Z) . (2.55)
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