CERN Program Library Long Writeup W5013 - CERNLIB ...

For the other charged particles the differential cross-section can be written:
dσ
dT = 2πZr2 0m 1 [
]
1
β 2 T 2 1 − β 2 T
for spin 0 particle
TMAX
dσ
dT = 2πZr2 0m 1 [
1
β 2 T 2 1 − β 2 T
TMAX + T 2 ]
2E 2 for spin 1/2 particle
where TMAX is the maximum energy transferable to the free electron:
TMAX =
2m(γ 2 − 1)
1+2γ(m/M)+(m/M) 2
and TCUT is the energy threshold for the δ-ray emission: TCUT ≤ T ≤ TMAX
2.2 Sampling
Apart from the normalisation, the cross-section can be written as
dσ
dɛ = f(ɛ)g(ɛ),
where, for e − e − scattering,
f(ɛ) = 1 ɛ 0
ɛ 2 1 − 2ɛ 0
[
]
4
g(ɛ) =
9γ 2 (γ − 1) 2 ɛ 2 − (2γ 2 ɛ
+2γ − 1)
− 10γ +5
1 − ɛ + γ2
(1 − ɛ) 2
and for e + e − scattering
f(ɛ) = 1 ɛ 2 ɛ 0
1 − ɛ 0
g(ɛ) = B 0 − B 1 ɛ + B 2 ɛ 2 − B 3 ɛ 3 + B 4 ɛ 4
B 0 − B 1 ɛ 0 + B 2 ɛ 2 0 − B 3ɛ 3 0 + B 4ɛ 4 0
Here B 0 = γ 2 /(γ 2 −1) and all the other quantities have been defined above. For the other charged particles:
f(T ) =
( 1
TCUT TMAX) − 1 1
T
g(T ) = 1− β 2 T
TMAX + T 2
2E 2
GDRAY samples the variable ɛ by:
1. sample ɛ from f(ɛ)
(last term for spin- 1 2
particle only)
2. calculate the rejection function g(ɛ) and accept the sampled ɛ with a probability of g(ɛ).
After the successful sampling of ɛ, GDRAY generates the polar angles of the scattered electron with respect
to the direction of the incident particle. The azimuthal angle φ is generated isotropically; the polar angle θ
is calculated from the energy momentum conservation. This information is used to calculate the energy and
momentum of both scattered particles and to transform them into the GEANT coordinate system.
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