THE EGS5 CODE SYSTEM

2.10 Møller Scattering
The form of the cross sections and the sampling methods that we use for modeling Møller and
Bhabha scattering follow those given by Messel and Crawford[103] (e.g., see p.13-14 therein) except
that various misprints have been corrected.
The differential Møller[109] cross section is given by
d˘Σ Møller (Ĕ0)
dĔ
= X 0n2πr 2 0 m
β 2 ˘T 2 0
[
C 1 + 1 E
( 1
2)
E − C + 1 ( )] 1
E ′ E ′ − C 2
(2.193)
where
Ĕ 0 = incident electron energy (MeV),
˘T 0 = Ĕ0 − m = incident kinetic energy (MeV),
Ĕ = energy of scattered electron (MeV),
˘T = kinetic energy of scattered electron (MeV),
E = ˘T / ˘T 0 = fraction of kinetic energy to scattered electron,
E ′ = 1 − E = fraction of kinetic energy remaining,
γ = Ĕ0/m,
C 1 = [(γ − 1)/γ] 2 ,
C 2 = (2γ − 1)/γ 2 ,
beta 2 = 1 − 1/γ 2 = (v/c) 2 ,
and where the other terms have been defined previously.
Because of the ambiguity in the identity of the initial and final electrons, the cross section is
symmetric with respect to the interchange of E with E ′ . Another consequence of this is that E is
restricted to lie in the interval (0, 1/2). It can be seen that Equation 2.193 is singular at E = 0 (also
at E ′ = 0 but the range of E ′ is now restricted to (1/2, 1)), and the total Møller cross section is
infinite. We get around this by considering as discrete collisions only Møller scattering interactions
for which the scattered electron acquire at least some threshold energy, A E (we also define the
threshold kinetic energy of T E = A E − m). Since the incoming electron energy is Ĕ0 + m and the
minimum final energy is 2A E , we see that the threshold initial electron energy at which a discrete
Møller scattering event can take place is given by
Ĕ Møller
T h
= 2A E − m = 2T E + m . (2.194)
Møller scattering interactions in which secondary electrons (δ–rays) are ejected with energies than
less A E are treated as part of the continuous energy loss process (see Section 2.13).
The integral of the Møller cross section over some energy range can be expressed as
∫ Ĕ2
Ĕ 1
d˘Σ Møller (Ĕ0)
dĔ
dĔ = X 0n2πr 2 0 m
β 2 ˘T 0
[C 1 (E 2 − E 1 ) + 1 E 1
− 1 E 2
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