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| Geant 3.16 | GEANT User's Guide | PHYS210 ##
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Author(s) : L. Urban Submitted: 10.11.84
Origin : GEANT2 Revised: 17.12.92
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|CALL GPRSGA |
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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, lambda= ((1)/(Sigma)) (in cm), as a function of the medium and the energy. For the pair production by photons, it calls the function GPRSGG. The energy binning is set within the array ELOW (COMMON CGMULO) in the routine GPHYSI. The following pointers are used:
GPRSGA is called at initialization 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.
+ - We have parameterized the total cross-section of e e -pair production by photon as:
sigma(Z, E )= Z(Z+ 1)(F (X) +F (X)Z +F (X)/ Z) (barn/atom) (1)
gamma 1 2 3
where X = ln(E /m),
gamma
m = electron mass,
E = photon energy
gamma
5 n
and F (X) = sum c X
i n=0 n
The parameters c were taken from a least-square fit to the data [bib-HUBB] and can be found in the DATA statement within the function GPRSGG(Z,E) which computes the formula (1) (in barn/atom).
This parameterization gives a good description of the data in the range:
1<=Z< =100
. 1.5 MeV<=E < =100GeV } ((Delta sigma)/ (sigma))<=5% with a mean value of' 2.2%
gamma
The mean free path, lambda, for a photon to interact via pair production is given by
lambda =1/ Sigma (2)
where Sigma is the macroscopic cross-section (1/cm). This quantity is given by
Sigma =((Nrhosigma(Z, E ))/(A)) (3)
gamma
and in the case of a compound or mixture:
Sigma =((Nrho sum p sigma(Z , E ))/(sum p A ))= Nrhosum (w /A )* sigma(Z ,E )(4)
i i i gamma i i i i i i i gamma
N Avogadro's number
Z(Z ) atomic number of the material (i'th component of the material)
i
A(A ) atomic weight of the material (i'th component)
i
rho density of the material
sigma total cross-section per atom for pair production
p proportion by number of the i'th element in the material
i
p ' w /A where w is the corresponding proportion by weight.
i i i i
This mean free path is tabulated at initialization time as a function of the medium and of the energy by the routine GPRSGA.