THE EGS5 CODE SYSTEM

and N g is a normalization factor that should be chosen so that
[
]
1
g(ξ) ≤ 1 ∀ ξ ∈
1 + E± 2 , 1 .
π2
The position of the maximum of the function g proved difficult to characterize accurately and
so a two-step iterative scheme was developed based upon the slow variation of the logarithmic term
[1+ln m(ξ)/4] in Equation 2.158 and the observation that the position of the maximum is relatively
independent of the value of r. For the purposes of estimating the maximum value of g, r is set
equal to 1, and a satisfactory algorithm for calculating N g is
[ ( ) ]
1
N g = 1.02 max g
1 + E±π 2 2 , g(ξ max)
(1) , (2.159)
where ξ max (1) is an estimate of the position of the maximum of g after a one-step iteration. The
zeroth-order estimate is:
ξ (0)
max = max
{
0.01, max
[
(
)
1
1 + E±π 2 2 , min 222
]} 0.5,
k 2 Z 1/3 ,
and the second iteration yields:
⎧ ⎡
⎛
√ ⎞⎤⎫
⎨
(
ξ max (1) = max
⎩ 0.01, max 1
⎣
1 + E±π 2 2 , min ⎝0.5, 1 2 − α′
α
3β ′ + ′ ) 2 sgn(α′ )
3β ′ + 1 ⎬
⎠⎦
4 ⎭
where
and
α ′ = 1 + ln m(ξ (0)
max)/4 − β ′ (ξ (0)
max − 1/2),
β ′ = ξ(0)
sgn(α ′ ) =
max(Z 1/3 /111) 2
2m(ξ (0)
max)
{
+1 if α ′ ≥ 0
−1 if α ′ < 0
.
The extra 1.02 in Equation 2.159 is a “safety factor”.
The Schiff threshold
The Schiff distribution breaks down mathematically for E γ < 4.14 MeV. To prevent non-physical
modeling, if a user has requested the Schiff distribution, the lowest order approximate distribution
of Equation 2.155 is used when the photon energy is less than the 4.14 MeV threshold.
A more complete discussion of pair angular distributions as adapted to the EGS code, may be
found documented elsewhere[26].
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