THE EGS5 CODE SYSTEM

d˘Σ P air, Run−time
dE
=
[
2
3 − 1
+
36 ln 183[1+(Z U if ˘k>50,Z P )]
[ (
)]
1 4
12 3 + 1
9 ln 183[1+(Z U if ˘k>50,Z P )]
) ] 2
×
[
12
(
E − 1 2
]
[1] C(δ ′ )
A(δ ′ ) . (2.145)
When these are divided by Ĕ0 and ˘k, respectively, they become
d˘Σ Brem, Run−time
d˘k
and
d˘Σ P air, Run−time
dĔ
which are computed by PEGS functions BREMDR and PAIRDR. In general the letter R, as the last
letter of a PEGS cross section function, means “run-time” function. PEGS may be used to plot
these for comparison with the more exact BREMDZ and PAIRDZ which evaluate Equations 2.43 and
2.44.
It will be observed that the pair production formulas are symmetric about E = 1/2. One of the
electrons will be given energy ˘kE and the other ˘k(1 − E). The choice of which one is a positron is
made randomly. Since we need to know which particle has the lower energy so we can put it on
the top stack position, we restrict the range of of E to (0,1/2) and double f 1 (E) and f 2 (E), thus
guaranteeing that any sampled value of E will correspond to the electron with the lower energy.
We thus sample f 1 (E) by letting E = 1/2ζ, and we sample f 2 (E) by letting
E = 1 2 (1 − max (ζ 1, ζ 2 , ζ 3 )) (2.146)
where the ζ values are drawn uniformly on the interval (0, 1) (see Section 2.2).
A special approximation which has been carried over from previous versions is that if the
incident photon has energy less than 2.1 MeV, one of the electrons is made to be at rest and the
other given the rest of the available energy. One reason for making this approximation is that
the pair sampling routine becomes progressively more inefficient as the pair production threshold is
approached. Perhaps a better approximation would be to pick the energy of the low energy electron
uniformly from the interval (m, ˘k/2).
We now conclude this section on bremsstrahlung and pair production with a few general remarks.
We first note that for δ ′ ≤ 1, that A(δ ′ ), B(δ ′ ) and C(δ ′ ) are all quadratic functions of δ ′ . The
three coefficients depend on whether the incident energy is above or below 50 MeV. For δ ′ > 1,
A(δ ′ ), B(δ ′ ) and C(δ ′ ) are equal and are given by
A, B, C(δ ′ ) = φ 1(δ ′ ) + 4
(Z V if Ĕ 0 , ˘k
)
> 50, Z G
φ 1 (0) + 4
(Z V if Ĕ 0 , ˘k
) (2.147)
> 50, Z G
which will have the form c 1 + c 2 ln(δ ′ + c 3 ). The A, B, C must not be allowed to go negative.
PEGS computes a maximum allowed ∆ E above which the A, B, C are considered to be zero.
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