THE EGS5 CODE SYSTEM

where
α ′ 1 =
α ′ 2 =
k 0
′
k 0 ′ + 1 , f 1 ′′ (E ′ ) = 2E ′ , E ′ ∈ (0, 1) (2.186)
1
k 0 ′ + 1 , f 2 ′′ (E ′ ) = 1, E ′ ∈ (0, 1) . (2.187)
Both of these sub-distributions are easily sampled.
To compute the rejection function it is necessary to get sin 2 θ. Let
t =
m(1 − E)
˘k 0 E
. (2.188)
Then using Equation 2.172, we have
cos θ = (˘k 0 + m)˘k − ˘k 0 m
˘k 0˘k
= 1 + mE − m
˘k 0 E
= 1 − t . (2.189)
Thus
sin 2 θ = 1 − cos 2 θ = (1 − cos θ)(1 + cos θ) = t(2 − t) . (2.190)
When the value of E is accepted, then sin θ and cos θ are obtained via
sin θ =
√
sin 2 θ (2.191)
cos θ = 1 − t . (2.192)
The sampling procedure is as follows:
1. Compute the parameters depending on ˘k 0 , but not E: k ′ 0 , E 0, α 1 , and α 2 .
2. Sample E in the following way: If α 1 ≥ (α 1 + α 2 )ζ 1 , use E = E 0 e α 1ζ 2
. Otherwise, use
E = E 0 + (1 − E 0 )E ′ , where E ′ is determined from
E ′ = max (ζ 3 , ζ 4 ) if k ′ 0 ≥ (k ′ 0 + 1)ζ 2
or from
E ′ = ζ 3 otherwise.
3. Calculate t and the rejection function g(E). If ζ 4 (or ζ 5 ) < g(E), reject and return to Step 2.
After determining the secondary energies, Equation 2.167 is used to obtain the scattering angles
and UPHI is called to select random azimuth and to set up the secondary particles in the usual way.
Note again that a more detailed treatment of Compton scattering is provided in section 2.18.
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