Materials with Z≤100

For media with $Z\; \le 100$

we use SANDIA parametrisation []. 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: $\mu$_ij= {C_1,ijE_γ}+{C_2,ijE_γ²}+{C_3,ijE_γ³}+{C_4,ijE_γ⁴} (cm²g^-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 $jth$

interval is calculated as: $\mu$_j= ∑_k=1^Nf_kμ_j,k

where $f$_k is the fraction by mass of $kth$ element in the material. Substituting () into () one finds that the cross-section coefficients can be calculated as: $C$_i,total= ∑_k=1^Nf_kC_i,jk

for i from 1 to 4. The macroscopic cross-section is calculated as follows: $\Sigma =\; \rho \mu \; (cm-1)$

where $\rho$ is the medium density.

As follows from () 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= Z₁+1 applying the weights $w$₁= Z₂-Z_x and $w$₂= Z_x-Z₁ respectively.