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| Geant 3.16 | GEANT User's Guide | PHYS230 ##
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Author(s) : L.Urban Submitted: 26.10.84
Origin : Same Revised: 17.12.92
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|CALL GPHOTI |
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GPHOTI calculates the total cross-section for the photoelectric effect. It tabulates the mean free path, lambda= ((1)/(Sigma)) (in cm), as a function of the medium and the energy [bib-STOR]. It calls the function GPHSIG for the total cross-section. The energy binning is set within the array ELOW (COMMON CGMULO) in the routine GPHYSI. GPHOTI is called at initialization time by GPHYSI.
VALUE = GPHSIG(Z,EGAM)
GPHSIG calculates the total cross-section for the photoelectric effect of a photon with energy EGAM in material with atomic number Z. It is called by GPHOTI.
The mean free path, lambda, for a photon to interact via photoelectric effect is given by
lambda =((1)/ (sum )) (in cm) (1)
where sum , the macroscopic cross-sectioni, for an element is given as
sum =((Nrhosigma(Z, E ))/(A)) in (1/cm) (2)
gamma
and for a compound or a mixture
sum =((Nrho sim sigma(Z ,E ))/(sim p A )) = Nrhosim (w /A )* rho(Z ,E )(3)
i gamma i i i i i gamma
where
N Avogadro's number
Z(Z ) atomic number (of i'th component) of the medium
i
A(A ) atomic number (of i'th component) of the medium
i
rho density
sigma total cross-section
p proportion by number of the i'th element in
i the material (p ' w / A wherew the corresponding
i i i i
proportion by weight).
For 5<=Z< =100 the binding energy of the inner shells have been parameterized as:
2 3
E (Z) =Z (A + B Z+ C Z + D Z ) MeV (4)
i i i i 2 i
where, i= K,L ,L are as following: I II
+------+------------------------------------------------------------
| | | | | |
+------+------A-------+------B------+-------C-------+------D-------+
| | | | | |
| K | 0.66644e-5 | 0.22077e-6 | -0.32552e-8 | 0.18199e-10 |
| L | -0.29179e-6 | 0.87983e-7 | - 0.12589e-8 | 0.69602e-11 |
| I | | | | |
| L | -0.68606e-6 | 0.10078e-6 | -0.14496e-8 | 0.78809e-11 |
+--II--+--------------+-------------+---------------+--------------+
| |
Then the cross-section of the photoeletric effect can be parameterized as:
2
(p /Z) +p X +p +p Z +(p / X)+p Z
1 2 3 2 5 3 6
+p (Z/X) +(p / X )+ (p Z )
7 8 9
2 2 3
+p (Z /X) +p (Z/ X )+ p (1/X )if E>E (Z)
alpha beta 10 11 12 k
sigma(Z, E)= Z X { (p /Z) +p X +p if E
X =m/ E ; sigma in barn/atom (6)
The fit was made over 301 data points chosen between
5<=Z< =100 and 10keV< =E<=50 MeV. The values of the parameters are put
in the DATA statement within the function
GPHSIG which compute the formula
(4) in barn/atom. The accuracy of the fit is estimated to be
Deltasigma/sigma<=25% near to the peaks, and Deltasigma/ sigma<=10%
elsewhere.