CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS220
Origin : G.N.Patrick, L.Urbán Submitted: 26.10.84
Revision : Revised: 16.12.93
Documentation :
1 Subroutines
Total cross-section for Compton scattering
CALL GCOMPI
GCOMPI calculates the total cross-section for Compton scattering. It tabulates the mean free path, λ = 1 Σ (in
cm), as a function of the medium and of the energy (see JMATE data structure). The energy binning is set
within the array ELOW (common /GCMULO/) in the routine GPHYSI. GCOMPI is called at initialisation time by
GPHYSI.
2 Method
The mean free path, λ, for a photon to interact via Compton scattering is given by
λ = 1 Σ = A 1
N Av ρ σ(Z, E)
where:
N Av Avogadro’s number
Z, A atomic and mass number of the medium
ρ density of the medium
σ total cross-section per atom for Compton scattering
E energy of the photon.
For the total cross-section an empirical cross-section formula is used which reproduces the cross-section
data rather well down to 10 keV:
[
log(1 + 2X)
σ(Z, E) =Z P 1 (Z) + P ]
2(Z)+P 3 (Z)X + P 4 (Z)X 2
X
1+aX + bX 2 + cX 3 barn atom −1
where
m = electron mass
X = E m
P i (Z) = D i + E i Z + F i Z 2
The values of the parameters are put in the DATA statement within the routine GCOMPI. The fit was made
over 511 data points chosen between:
1 ≤ Z ≤ 100 ; 10 keV ≤ E ≤ 100 GeV
The accuracy of the fit is estimated to be:
∆σ
σ
= ⎧
⎨
⎩
≈ 10% for E ≃ 10 keV − 20 keV
≤ 5 − 6% for E > 20 keV
216 PHYS220 – 1