CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS331
Origin : D. Ward, L.Urbán Submitted: 26.10.84
Revision : Revised: 16.12.93
Documentation :
1 Subroutines
Simulation of the delta-ray production
CALL GDRAY
GDRAY generates explicitly the delta-rays (see [PHYS330] for treatment of the ionization as continuous
energy loss and for the calculation of the total cross-section).
input:
output:
common /GCTRAK/
common /GCKING/
The routine is called from the tracking routines GTELEC, GTMUON, GTHION and GTHADR when a charged
particle reaches its interaction point.
2 Method
2.1 Differential cross-section
The differential cross-section of the δ-ray production can be written as in equations (1, 2) [54], [12], [55].
For the electron/electron (Möller) scattering we have:
dσ
dɛ =
2πZr2 0 m
[
(γ − 1)
2
β 2 (E − m) γ 2 + 1 ( 1
ɛ ɛ − 2γ − 1 )
γ 2 + 1 ( ) 1 2γ − 1
]
1 − ɛ 1 − ɛ γ 2 (1)
and for the positron-electron (Bhabha) scattering:
dσ
dɛ = 2πZr2 0 m [ 1
(E − m) β 2 ɛ 2 − B ]
1
ɛ + B 2 − B 3 ɛ + B 4 ɛ 2
(2)
where
Z = atomic number of the medium E = energy of the incident particle
M = rest mass of the incident particle γ = E M
β 2 = 1− 1 1
γ 2 y =
γ +1
B 1 = 2− y 2 B 2 = (1− 2y)(3 + y 2 )
B 3 = (1− 2y) 2 +(1− 2y) 3 B 4 = (1− 2y) 3
ɛ =
T
E − m
with T the kinematic energy of the scattered electron (of the lower energy in the case of e − e + scattering).
The kinematical limits for the variable ɛ are:
ɛ 0 =
TCUT
E − m ≤ ɛ ≤ 1 2 for e− e − ɛ 0 = TCUT
E − m ≤ ɛ ≤ 1
256 PHYS331 – 1
for e+ e −