THE EGS5 CODE SYSTEM

defined by
δ ij = 1 if i = j,
0 otherwise. (2.42)
Using this notation, we start with the following formulas for the bremsstrahlung and pair production
differential cross sections: 5 .
dσ Brem (Z, Ĕ0, ˘k)
= A′ (Z, Ĕ0)r0 2 αZ(Z + ξ(Z))
{ d˘k
˘k
(
× 1 + (Ĕ/Ĕ0) 2) [ φ 1 (δ) − 4 ]
3 ln Z − (4f c(Z) if Ĕ 0 > 50, 0)
and
− 2 3
( ) [ Ĕ
φ 2 (δ) − 4 ] }
Ĕ 0
3 ln Z − (4 f c(Z) if Ĕ 0 > 50, 0)
(2.43)
dσ P air (Z, ˘k, Ĕ + )
= A′ p (Z, ˘k)r0 2 αZ(Z + ξ(Z))
dĔ+
˘k
{ 3
(Ĕ2
× + + −) [
Ĕ2 φ 1 (δ) − 4 ]
3 ln Z − (4f c(Z) if ˘k > 50, 0)
+ 2 [
3 Ĕ+Ĕ− φ 2 (δ) − 4 ]}
3 ln Z − (4 f c(Z) if ˘k > 50, 0)
(2.44)
where
and
∆ =
=
˘km
2Ĕ0Ĕ
˘km
2Ĕ+Ĕ−
δ = 136 Z −1/3 2∆ (2.45)
(for bremsstrahlung) (2.46)
(for pair production) . (2.47)
To avoid confusion it should be noted that our δ is the same as the δ of Butcher and Messel[39] but
we use φ i (δ) to denote their f i (δ). Rossi[141] and Koch and Motz[91] use a variable γ = 100
136δ. Also,
note that our φ i (δ) has the same value as the φ i (γ) of Koch and Motz[91] (e.g., see their Figure 1)
provided “our δ” = 136
100 times “their γ.” For arbitrary screening, φ 1 and φ 2 are given by
φ 1 (δ) = 4
φ 2 (δ) = 4
∫ 1
∆
∫ 1
∆
(q − ∆) 2 [1 − F (q, Z)] 2 dq
q 3 + 4 + 4 ln Z , (2.48)
3
[
( ]
q
q 3 − 6∆ 2 q ln + 3∆
∆) 2 q − 4∆ 3
× [1 − F (q, Z)] 2 dq
q 4 + 10 3 + 4 ln Z (2.49)
3
5 As described earlier, we have adopted the notation that cupped energy variables (e.g., Ĕ) are in MeV and cupped
distance variables (e.g., ˘t) are in radiation lengths. Uncupped variables are in CGS units and constants are defined
explicitly
39