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 ofx = 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, maybe found documented elsewhere[29].2.7.2 Pair Angle SamplingIn previous versions of EGS, both particles in all newly created e − e + pairs were set in motion atfixed angles Θ ± with respect to the initiating photon direction. Θ ± , the scattering angle of thee + or e − (in radians), is of the form Θ ± = 1/k where k is the energy of the initiating photon inunits of m o c 2 , the rest mass of the electron. Defined in this way, Θ ± provides an estimate of theexpected average scattering angle 6 .The motivation for employing such a crude approximation is as follows: At high energies thedistribution is so strongly peaked in the forward direction that more accurate modeling will not significantlyimprove the shower development. At low energies, particularly in thick targets, multiplescattering of the resultant pair as the particles slow will “wash out” any discernible distribution inthe initial scattering angle. Therefore, the extra effort and computing time necessary to implementpair angular distributions was not considered worthwhile. It was recognized, however, that theabove argument would break down for applications where the e + e − pair may be measured beforehaving a chance to multiple scatter sufficiently and obliterate the initial distribution, and this wasindeed found to be the case.To address this shortcoming, two new options for sampling the pair angle were introduced, asdescribed in the two following subsections. Procedures for sampling these formulas are given inthe next sections. The formulas employed in this report were taken from the compilation by Motz,Olsen and Koch[111].Leading order approximate distributionAs a first approximation, the leading order multiplicative term of the Sauter-Gluckstern-Hull formula(Equation 3D-2000 of Motz et al.[111]) was used:dPdΘ ±=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 distributionshould peak at Θ ± = 1/( √ 3E ±). However, the Bethe-Heitler cross section used in EGS5 peaks at E ± = k/2 andthe approximation Θ ± = 1/k is a reasonable one on average, given the highly approximate nature of the angularmodeling.57