THE EGS5 CODE SYSTEM

at either x = 0, x = (πE 0 ) 2 (i.e., at the minimum or maximum values of x), or in the vicinity of
x = 1. Therefore, the rejection function normalization was chosen to be:
N r = {max[g(0), g(1), g((πE 0 ) 2 )]} −1 . (2.154)
A more complete discussion of bremsstrahlung angular distributions as adapted to EGS, may
be found documented elsewhere[29].
2.7.2 Pair Angle Sampling
In previous versions of EGS, both particles in all newly created e − e + pairs were set in motion at
fixed angles Θ ± with respect to the initiating photon direction. Θ ± , the scattering angle of the
e + or e − (in radians), is of the form Θ ± = 1/k where k is the energy of the initiating photon in
units of m o c 2 , the rest mass of the electron. Defined in this way, Θ ± provides an estimate of the
expected average scattering angle 6 .
The motivation for employing such a crude approximation is as follows: At high energies the
distribution is so strongly peaked in the forward direction that more accurate modeling will not significantly
improve the shower development. At low energies, particularly in thick targets, multiple
scattering of the resultant pair as the particles slow will “wash out” any discernible distribution in
the initial scattering angle. Therefore, the extra effort and computing time necessary to implement
pair angular distributions was not considered worthwhile. It was recognized, however, that the
above argument would break down for applications where the e + e − pair may be measured before
having a chance to multiple scatter sufficiently and obliterate the initial distribution, and this was
indeed found to be the case.
To address this shortcoming, two new options for sampling the pair angle were introduced, as
described in the two following subsections. Procedures for sampling these formulas are given in
the next sections. The formulas employed in this report were taken from the compilation by Motz,
Olsen and Koch[111].
Leading order approximate distribution
As a first approximation, the leading order multiplicative term of the Sauter-Gluckstern-Hull formula
(Equation 3D-2000 of Motz et al.[111]) was used:
dP
dΘ ±
=
sin Θ ±
2p ± (E ± − p ± cos Θ ± ) 2 , (2.155)
6 The extremely high-energy form of the leading order approximation discussed later implies that the distribution
should peak at Θ ± = 1/( √ 3E ±). However, the Bethe-Heitler cross section used in EGS5 peaks at E ± = k/2 and
the approximation Θ ± = 1/k is a reasonable one on average, given the highly approximate nature of the angular
modeling.
57