CERN Program Library Long Writeup W5013 - CERNLIB ...

VALUE = GPHSG1 (EGAM)
GPHSG1 calculates the total cross-section for photoelectric effect. It is called by GPHOTI for Z ≤ 100.
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 > 100. It is called by GPHOTI.
2 Method
2.1 Materials with Z ≤ 100
For media with Z ≤ 100 we use SANDIA parametrisation [19]. The cross-section for elements was
fitted with a linear combination of reciprocal powers of the photon energy E γ (E γ in keV). The fits were
performed in different intervals j of the photon energy. In such an interval the cross-section reads as:
µ ij = C 1,ij
E γ
+ C 2,ij
E 2 γ
+ C 3,ij
E 3 γ
+ C 4,ij
E 4 γ
(cm 2 g −1 ) (1)
with j changing from 1 to m i , where m i is the number of fitting intervals used for element i.
For the composites or mixtures of N elements the cross-section for j th interval is calculated as:
µ j =
N∑
f k µ j,k (2)
k=1
where f k is the fraction by mass of k th element in the material. Substituting (1) into (2) one finds that the
cross-section coefficients can be calculated as:
N∑
C i,total = f k C i,jk (3)
k=1
for i from 1 to 4. The macroscopic cross-section is calculated as follows:
Σ=ρµ (cm −1 ) (4)
where ρ is the medium density.
As follows from (3) each compound is decomposed to its components which should coincide with chemical
elements. If this is not the case i.e. a component has a non-integer atomic number Z x and is created by a
call to GSMATE then the cross-section constants are calculated using two elements with Z 1 = integer(Z x )
and Z 2 = Z 1 +1applying the weights w 1 = Z 2 − Z x and w 2 = Z x − Z 1 respectively.
2.2 Materials with Z > 100
Originally the parametrisation described below was developed for the elements with the atomic number Z
between 5 and 100. Lacking more accurate data and assuming that there are no dramatic changes of the
cross-section behaviour this method (i.e. GPHSIG function) is used for Z > 100.
The macroscopic cross-section for an element is given by
Σ= Nρσ(Z, E γ)
(cm −1 ) (5)
A
and for a compound or a mixture
Σ= Nρ∑ i σ(Z i,E γ )
∑
i n iA i
= Nρ ∑ i
p i
A i
σ(Z i ,E γ ) (cm −1 ) (6)
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