+-------------+ +----------## | Geant 3.16 | GEANT User's Guide | PHYS230 ## +-------------+ +----------##
Author(s) : L.Urban Submitted: 26.10.84 Origin : Same Revised: 17.12.92
+--------------------------------+ |CALL GPHOTI | +--------------------------------+
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.