CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS351
Origin : L.Urbán Submitted: 26.10.84
Revision : G.Azuelos Revised: 16.12.93
Documentation :
1 Subroutines
Simulation of e+e- annihilation
CALL GANNI
GANNI generates the annihilation of a positron into either one or two photons. It uses the following input
and output:
input:
output:
via common /GCTRAK/
via common /GCKING/
The routine is called automatically from the tracking routine GTELEC, when the positron reaches its interaction
point during the tracking.
CALL GANNIR
GANNIR generates the positron annihilation at rest. It is called from the tracking routine GTELEC, if the
positron energy is below the cut-off energy CUTELE in common block /GCCUTS/.
2 Method
The type of annihilation is sampled from the total cross-sections for the annihilation into two photons and
into one photon (see section [PHYS350]).
Annihilation into two photons
The differential cross-section of the two-photon positron-electron annihilation can be written as [79, 12]:
dσ(Z, ɛ)
dɛ
= ma[S(aɛ)+S(a(1 − ɛ))] (1)
where m is the electron mass Z is the atomic number of the material. If we indicate with E the initial
energy of the positron, with r 0 the classical electron radius and with k the energy of the less energetic
photon generated, we have:
γ = E m
k
ɛ =
E + m
Zπr0
2 C 1 =
a(E − m)
a = γ +1
[
S(x) = C 1 −1+ C 2
x − 1 ]
x 2
C 2 = a + eγ a
The kinematical limits for the variable ɛ are:
ɛ 0 =
1
a + √ γ 2 − 1 ≤ ɛ ≤ 1 2
288 PHYS351 – 1