THE EGS5 CODE SYSTEM

For φ rad in the completely screened electron field Koch and Motz[91] (formula III-8 on p. 949) give
φ rad,electron = 4αr0 2 Z ln (530 Z −2/3 ) . (2.56)
On the other hand, from the formulas of Bethe and Ashkin[24] mentioned above, one would expect
φ rad,electron = 4αr0 2 Z ln (1440 Z −2/3 ) .
Tsai’s work[172] has dealt with these problems more accurately. We have not switched to his
method but continue to define a single parameter, ξ, which is used in a simple Z(Z + ξ) correction
to the cross sections to account for electron effects. However, we have redefined ξ making use of
Tsai’s radiation logarithms:
L ′ rad
ξ(Z) =
(Z)
(2.57)
L rad (Z) − f c (Z)
where
⎧
ln1194 Z −2/3 if Z > 4
⎪⎨ 6.144 if Z = 1
L ′ rad = 5.621 if Z = 2
⎪⎩ 5.805 if Z = 3
5.924 if Z = 4
⎧
ln184.15 Z −1/3 if Z > 4
⎪⎨ 5.310 if Z = 1
L rad = 4.790 if Z = 2
⎪⎩ 4.740 if Z = 3
4.710 if Z = 4
These expressions are used by function XSIF of PEGS to compute ξ(Z) for use in Equations 2.43
and 2.44. These definitions replace the simpler ln1440 Z −2/3 and ln183 Z −1/3 used in PEGS3.
Note that for the rest of this chapter, “183” is a variable name representing the value 184.15, and
similarly, “1440” represents 1194.
We have also changed the definition of radiation length to that of Tsai[172]:
X0 −1 = N aραr0
2 [
]
Z 2 [L rad (Z) − f c (Z)] + ZL ′
A
rad(Z) . (2.58)
This change has a considerable effect on X 0 for very light elements (a 9% increase for hydrogen)
but only a small effect for Z ≥ 5.
We have done several comparisons between the pair production cross sections used in PEGS
and the more accurate results of Tsai. In general, they agree to within a few percent except for
very low Z (< about 10) elements at energies below 1 GeV.
Now that we have discussed all items appearing in Equations 2.43 and 2.44, we need to mention
some additional corrections to Equation 2.43 which are neglected in EGS5. First, the differential
42