THE EGS5 CODE SYSTEM

Angular distribution formulas
The formula employed for the angular sampling routine is 2BS of Koch and Motz[91], which is the
cross section, differential in photon energy and angle,
dσ k,Θ = 4Z2 r0
2 {
dk 16y 2
137 k ydy E
(y 2 + 1) 4 − (E 0 + E) 2 [
E
2
E 0 (y 2 + 1) 2 E0
2 + 0 + E 2 4y 2 ] }
E
(y 2 + 1) 2 E0
2 −
(y 2 + 1) 4 ln M(y) ,
E 0
(2.149)
where,
( ) (
1 k 2
y = E 0 Θ;
M(y) = Z 1/3 ) 2
+
2E 0 E 111(y 2 ,
+ 1)
and, the following definitions for the variables apply:
k energy of the photon in units of m e c 2
Θ angle between the outgoing photon and the incoming electron direction (in radians)
Z atomic number of the target material
r 0 ≡ e 2 /m e c 2 (classical electron radius)
E 0 , E initial and final electron energy in units of m e c 2
The following table, copied from the Koch and Motz article, outlines the essential approximations
employed in the derivation of Equation 2.149.
Approximation
Condition of validity
i) Approximate screening potential (Ze/r)e −r/a
ii) Born approximation (2πZ/137β 0 ), (2πZ/137β) ≪ 1
iii) Extreme relativistic E 0 , E, k ≫ 1
iv) Small angles sin Θ = Θ
v) Approximate e − angular integration Θ < (Z 1/3 /111E 0 )
It should be noted that only the angular distribution part of Equation 2.149 is employed. The
cross section differential in photon energy employed by the EGS5 code is far less restrictive (Approximation
(iii) plus Thomas-Fermi screening factors). For the purposes of modeling electron linacs,
the ultimate test of these approximations is comparison with experiment. In this regard, Koch and
Motz present encouraging data (their Figure 17) which exhibits excellent agreement between experiment
and Equation 2.149 for 4.54 MeV electrons on Au. Although use of Equation 2.149 violates
constraints ii), iii) and iv) in the cases they showed, the deviation was at worst 10% (at large angles)
and usually much better. In particular, violating the Born approximation constraints seemed not
especially deleterious to the comparison. The conditions of this experiment are similar to those
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