+-------------+ +----------##
| Geant 3.12 | GEANT User's Guide | Phys250 ##
+-------------+ +----------##
Author(s) : G.Tromba, P.Bregant Submitted: 10.10.89
Origin : Same Revised: 17.12.92
+--------------------------------+
|CALL GRAYLI |
+--------------------------------+
GRAYLI computes the mean free path, lambda, 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. The energy binning E is set within the i
array ELOW (COMMON GCMULO) in the routine GPHYSI. GRAYLI considers only the energy range defined as: ELOW(1)<=E < =ELOW(NEK1) where NEK1 is i defined by the data record RANGE (the default is 31). GRAYLI is called at initialization time by GPHYSI.
The mean free path, lambda, for Rayleigh scattering is given by lambda= ((1)/(Sigma)). For a simple material Sigma is defined as follows:
Sigma =((Nrho)/ (A))sigma (Z,E) (1)
c
where:
N Avogadro's number Z,A atomic number and weight of the medium rho density of the medium sigma total atomic coherent scattering cross-section E c energy of the photon.
For a mixture or a compound Sigma is defined as:
Sigma =Nrho sum ((W )/(A ))sigma (Z ,E) (2)
i i i c i
i
where:
th
W percentual weight of the i element
i
th
Z ,A atomic number and weight of the i element
i i
rho density of the medium
sigma total atomic coherent scattering cross-section of
c th
i i element.
An empirical cross-section is used to produce the total cross-section data [bib-EGS3], [bib-HUB1]:
3 2
sigma (Z, E)= aE + bE + cE+ d barn/atom (3)
c
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 ((Deltasigma)/(sigma))= 10%, but it is better for most of the elements.
Different empirical formulae are used to produce the atomic form factor F(Z,E) data [bib-STOR]. For Z=1,99 the empirical expression is:
7 6 5 4 3 2
F(Z, E)= a E + b E + c E + d E +e E +f E +g E +h (4)
1 1 1 1 1 1 1 1
for Z=100 the formula used is:
5 4 3 2
F(Z, E)= a E + b E + c E + d E +e E +f (5)
2 2 2 2 2 2
for the other elements F is calculated as:
3 2 1
a E + b E + c E + d ifE< =E
F(Z, E)= { 3 3 3 3 c . (6)
3 2 1
a E + b E + c E + d ifE>E
4 4 4 4 c
The value of the energy E depends on Z and it is set in the array ELIM. c 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 ((Deltasigma)/(sigma))= 10% for E<=1MeV for most of the elements.
A(E ) is defined as follows: i
E E
i 2 i 2 2
A(E ) =2 int |F (E)| EdE =int |F (E)| dE (7)
i 0 T 0 T
where F (E) is the total atomic form factor which is function of the T energy E.