THE EGS5 CODE SYSTEM

2.16.2 Photoelectron Angular Distribution
In previous versions of EGS newly created photoelectrons were set in motion in the same direction
as the initiating photon. This proved to be too approximate for some applications, and so to address
this shortcoming, EGS4 was modified by Bielajew and Rogers to use the theory of Sauter[145] to
determine photoelectron angles. Empirical justification for the use of this distribution has been
given by Davisson and Evans[50], who showed that it applies even in the non-relativistic realm,
despite being derived for relativistic electrons. The implementation of a non-relativistic formula
due to Fischer[58] did not significantly impact simulation results, and so Sauter’s formula has been
applied universally in the EGS code.
Sampling the Sauter angular distribution
The Sauter distribution[145] as given by Davisson and Evans[50] may be integrated over the azimuthal
angle and cast in the form:
where
f(µ)dµ = 1 − µ2
[1 + K(1 − βµ)]dµ (2.401)
(1 − βµ)
4
µ = cos Θ
β = v/c
√
γ = 1/ 1 − β 2
K = (γ/2)(γ − 1)(γ − 2).
Here µ is the cosine of the angle that the electron is ejected (with respect to the initiating photon
direction), β is the speed of the electron relative to the speed of light and γ is the familiar relativistic
factor. Although Equation 2.401 may be integrated easily, its integral can not be inverted
analytically and so a direct sampling approach is not feasible. In addition, equation 2.401 may also
be very sharply peaked in the forward direction, making rejection sampling inefficient. Therefore,
we employ a mixed technique to sample for photoelectron angles. We make the separation:
where
is the directly sampled part, and
g(µ) =
f(µ) = g(µ)h(µ) (2.402)
1
[1 + K(1 − βµ)] (2.403)
(1 − βµ) 3
h(µ) = 1 − µ2
1 − βµ
(2.404)
is sampled via the rejection method. g(µ) and h(µ) may be easily normalized so that ∫ 1
−1 g(µ)dµ = 1
and h(µ) ≤ 1 for all µ, resulting in efficient sampling. A more complete discussion of photoelectron
angular distributions as adapted for EGS may be found elsewhere[30].
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