CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS210
Origin : L. Urbán Submitted: 10.11.84
Revision : Revised: 16.12.93
Documentation :
1 Subroutines
Total cross-section for e+e- pair production by photons
CALL GPRSGA
GPRSGA calculates the total cross-section for the pair production of photons and the direct pair production
of muons in all materials. It tabulates the mean free path, λ =1/Σ (in cm), as a function of the medium and
the energy. For the pair production by photons, it calls the function GPRSGG. The energy bins are the one of
the array ELOW in common /CGMULO/ initialised in the routine GPHYSI. The following pointers are used:
JMA = LQ(JMATE-I)
JPAIR = LQ(JMA-10)
pointer to the I th material
pointer to pair production cross-sections
GPRSGA is called at initialisation time by GPHYSI.
VALUE = GPRSGG (Z,E)
GPRSGG calculates the total cross-section for the pair production of a photon with energy E in material with
atomic number Z. It is called by GPRSGA.
2 Method
We have parameterised the total cross-section of e + e − -pair production by photon as:
σ(Z, E γ )=Z(Z +1)(F 1 (X)+F 2 (X)Z + F 3 (X)/Z) (barn/atom) (1)
where
X = ln(E γ /m),
m = electron mass,
E γ = photon energy
and
F i (X) =
5∑
c n X n
n=0
The parameters c n were taken from a least-square fit to the data [9] and can be found in the DATA statement
in the function GPRSGG(Z,E) which computes the formula (1) (in barn/atom).
This parameterisation gives a good description of the data in the range:
1 ≤ Z ≤ 100
1.5 MeV ≤ E γ ≤ 100 GeV
}
∆ σ
σ
≤ 5% with a mean value of ≈ 2.2% (2)
This mean free path is tabulated at initialisation as a function of the medium and of the energy by the routine
GPRSGA.
211 PHYS210 – 1