CERN Program Library Long Writeup W5013 - CERNLIB ...

Geant 3.16 GEANT User’s Guide PHYS250
Origin : G.Tromba, P.Bregant Submitted: 10.10.89
Revision : Revised: 16.12.93
Documentation :
1 Subroutines
Total cross-section for Rayleigh scattering
CALL GRAYLI
GRAYLI computes the mean free path, λ, for Rayleigh scattering as a function of the medium and of the energy.
It evaluates also an integral of atomic form factors which is used in the routine GRAYL (see [PHYS251])
to sample the scattering angles. GRAYLI is called during initialization by GPHYSI.
2 Method
2.1 Total cross-section
An empirical cross-section is used to produce the total cross-section data [12, 33]:
σ c (Z, E) =aE 3 + bE 2 + cE + d barn/atom (1)
The values of the coefficients are stored in the DATA statement within the routine GRAYLI. For each element
the fit was obtained over 27 experimental values of the total coherent cross-section. The accuracy of the fit
is estimated to be about ∆σ/σ ≈ 10%, but it is better for most of the elements.
2.2 The atomic form factors
Different empirical formulae are used to produce the atomic form factor F(Z,E) data [34]. For Z =1−
3, 91 − 99 the empirical expression is:
F (Z, E) =a 1 E 7 + b 1 E 6 + c 1 E 5 + d 1 E 4 + e 1 E 3 + f 1 E 2 + g 1 E + h 1 (2)
for Z=100 the formula used is:
F (Z, E) =a 2 E 5 + b 2 E 4 + c 2 E 3 + d 2 E 2 + e 2 E + f 2 (3)
for the other elements F is calculated as:
{
a3 E
F (Z, E) =
3 + b 3 E 2 + c 3 E + d 3 if E ≤ E c
a 4 E 3 + b 4 E 2 (4)
+ c 4 E + d 4 if E>E c
The value of the energy E c depends on Z and it is set in the array ELIM. The values of the coefficients
are stored in the DATA statement in the routine GRAYLI. For each element the fits were performed over 97
tabulated values of the form factors. The accuracy of the fit is estimated to about ∆σ/σ = 10% for E ≤ 1
MeV for most of the elements. The integral over the atomic form factors A (E i ) is defined as follows:
∫ Ei
∫
A (E i )=2 |F T (E)| 2 Ei
EdE = |F T (E)| 2 dE 2 (5)
0
0
where F T (E) is the total atomic form factor which is function of the energy E.
229 PHYS250 – 1