THE EGS5 CODE SYSTEM

+ 1 E 2
′ − 1 E 1
′
− C 2 ln E 2E 1
′ ]
E 1 E 2
′
(2.195)
where
and other symbols are the same as in Equation 2.193.
E i = (Ĕi − m)/ ˘T 0 , i = 1, 2 , (2.196)
E ′ i = 1 − E i , i = 1, 2 , (2.197)
The minimum and maximum energies for the scattered electron (by convention, the scattered
electron is taken to be the one which emerges with the lower energy) are A E and ˘T 0
2
+m, respectively.
When these limits are used for Ĕ1 and Ĕ2 in Equation 2.195, we obtain for the total discrete Møller
cross section (which we assume to non-zero only for Ĕ0 > ĔMøller T h
):
˘Σ Møller, Total (Ĕ0) == Equation 2.195 with Ĕ1 = A E and Ĕ2 = ( ˘T 0 /2) + m . (2.198)
PEGS functions AMOLDM, AMOLRM, and AMOLTM evaluate Equations 2.193, 2.195, and 2.198, respectively.
In sampling for the resultant energy, we use the variable E = ˘T / ˘T 0 and obtain
d˘Σ Møller (Ĕ0)
dE
= X 0n2πr 2 0 m
˘T 0 E 0
f(E)g(E) (2.199)
where
E 0 1
f(E) =
1 − 2E 0 E 2 , E ∈ (E 0, 1/2), (2.200)
g(E) = g 1 [1 + g 2 E 2 + r(r − g 3 )], (2.201)
E 0 = T E / ˘T 0 , (2.202)
g 1 = (1 − 2E 0 )/β 2 , (2.203)
g 2 = (γ − 1) 2 /γ 2 , (2.204)
g 3 = (2γ − 1)/γ 2 , (2.205)
r = E/(1 − E) . (2.206)
The sampling procedure is as follows:
1. Compute parameters depending on Ĕ0, but not E: E 0 , g 1 , g 2 , and g 3 .
2. Sample E from f(E) by using
E = T E / [ ˘T 0 − (Ĕ0 − ĔMøller T h
)ζ 1 ]). (2.207)
3. Compute r and the rejection function g(E). If ζ 2 > g(E), reject and return to Step 2.
After the secondary energies have been determined, Equation 2.167 can be used to obtain the
scattering angles, and EGS routine UPHI can be called to select random azimuthal angles and set
up the secondary particles in the usual way.
67