CERN Program Library Long Writeup W5013 - CERNLIB ...

E bind
, eV
10 5 10 20 30 40 50 60 70 80 90 100
10 4
10 3
E bind
=0.5 (Z α) 2 m e
K-shell energies
10 2
Z
Figure 41: Comparison between the K-shell binding energies given by the expression in the text and the
tabulated values.
Due to the symmetry of the formula (1) in ɛ, the range of ɛ can be expanded from (ɛ 0 , 1/2)to(ɛ 0 , 1−ɛ 0 ) and
the second function S can be eliminated from the formula. Having done this, the differential cross-section
can be decomposed (apart from the normalisation) as:
dσ
dɛ = 1
1
ln 1−ɛ 0
ɛ
ɛ
} {{ 0
}
f(ɛ)
(a 2 +2a − 2) − a 2 ɛ − 1 ɛ
a 2 − 2
} {{ }
g(ɛ)
(2)
Using the expression (2) with random numbers r i ∈]0, 1[,i =1, 2, the secondary photon energy is sampled
by the following steps:
1. sample ɛ from f(ɛ):
[ ( ) ] 1 − ɛ0
ɛ = ɛ 0 exp ln r 1
ɛ 0
(3)
2. compute the rejection function g(ɛ) and
(a) if r 2 ≤ g(ɛ) accept ɛ
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