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 $\Sigma =\; \{\; N\; \rho \sigma (Z,E$_γ) A} (cm^-1)

and for a compound or a mixture $\Sigma =\{\; N\; \rho \sum$_iσ(Z_i, E_γ)∑_in_iA_i}= N ρ∑_i{p_iA_i}σ( Z_i,E_γ) (cm^-1)

where

$N$	Avogadro's number
$Z(Z$i)	atomic number (of $ith$ component) of the medium
$A(A$i)	atomic mass (of $ith$ component) of the medium
$\rho$	density
$\sigma$	cross-section
$n$i	proportion by number of the $ith$ element in the material ($n$i= W pi/Ai where $p$i is the corresponding proportion by weight and $W$ is the molecular weight).

The binding energy of the inner shells has been parameterised as: $E$_i(Z) = Z²(A_i+ B_iZ + C_iZ²+ D_iZ³) &quad;MeV

where, $i\; =\; K,\; L$_I, L_II and the constants $A$_i, B_i, C_i and $D$_i

are tabulated below.

	1c|A	1c|B	1c|C	1c|D
K	0.66644$10-5$	0.22077$10-6$	-0.32552$10-8$	0.18199$10-10$
$L$I	-0.29179$10-6$	0.87983$10-7$	-0.12589$10-8$	0.69602$10-11$
$L$II	-0.68606$10-6$	0.10078$10-6$	-0.14496$10-8$	0.78809$10-11$

The photoelectric effect total cross-section has been parameterised as:

where X is the ratio of the electron mass to the incident photon energy and $\sigma$ is expressed in barns/atom.
The fit was made over 301 data points chosen between . The values of the parameters are put in a DATA statement within the function GPHSIG which computes the formula (). The accuracy of the fit is estimated to be

$\{\Delta \sigma \}\le$

$25$	$near\; to\; the\; peaks$
$10$	$elsewhere.$

$.$