THE EGS5 CODE SYSTEM

This agrees with formula (10) of Butcher and Messel[39] (except that they use Z AB = Z A + Z B and
do not use Z F in their X 0 definition), since our Z A , Z B , Z P are the same as their a, b, p. Now
ignoring the factor preceding the {} in Equation 2.98, noting that we require ˘k > A P (the photon
energy cutoff) and also that energy conservation requires ˘k < Ĕ0 − m, we obtain the factorization
(see Equation 2.64)
⎛
⎞
α 1 = ln 2 ⎝ 4 3 + 1
[
] ⎠ , (2.100)
9 ln 183 1 + (Z U if Ĕ 0 > 50, Z P )
f 1 (E) = 1 ( ) 1 − E
for E ∈ (0, 1) , (2.101)
ln 2 E
(
g 1 (E) = A ( δ ′ (E) ) (
) )
if EĔ0 ∈ A P , Ĕ 0 − m , 0 , (2.102)
α 2 = 1 2 , (2.103)
f 2 (E) = 2E for E ∈ (0, 1) , (2.104)
(
g 2 (E) = B ( δ ′ (E) ) )
if EĔ0 ∈ (A P , Ĕ0 − m), 0 . (2.105)
We notice that f 2 (E) is properly normalized, but that ( f 1 (E) has ) infinite integral over (0,1). Instead
we limit the range over which f 1 (E) is sampled to 2 −N Brem, 1 , where N Brem is chosen such that
To sample f 1 (E) we further factor it to
2 −N Brem
≤ A P
Ĕ 0
< 2 −(N Brem−1)
. (2.106)
f 1 (E) =
N∑
Brem
j=1
α 1j f 1j (E) g 1j (E) (2.107)
where
f 1j (E) =
( 1
ln 2 2j−1 if E < 2 −j 1
,
ln 2
The f 1j are properly normalized distributions.
α 1j = 1 , (2.108)
(1 − E2 j−1 )
E
if E ∈
(
2 −j , 2 −j+1) )
, 0 , (2.109)
g 1j (E) = 1 . (2.110)
We sample f 2 (E) by selecting the larger of two uniform random variables (see Section 2.2);
namely,
E = max (ζ 1 , ζ 2 ) , (2.111)
where ζ 1 and ζ 2 are two random numbers drawn uniformly on the interval (0, 1). To sample f 1 (E),
we first select the sub-distribution index
j = Integer Part (N Brem ζ 1 ) + 1 . (2.112)
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