Method

The mean free path, $\lambda$ , for a photon to interact via Compton scattering is given by

$\lambda =\; \{1\Sigma \}=\; \{AN$_Avρ}{1σ(Z,E)}

where:

$N$Av		$Avogadro\text{'}s\; number$
$Z,A$		$atomic\; and\; mass\; number\; of\; the\; medium$
$\rho$		$density\; of\; the\; medium$
$\sigma$		$total\; cross-section\; per\; atom\; for\; Compton\; scattering$
$E$		$energy\; of\; the\; photon.$

For the total cross-section an empirical cross-section formula is used which reproduces the cross-section data rather well down to 10 keV:

$\sigma (Z,E)\; =\; Z\; [\; P$₁(Z) {log(1+2X)X}+{P₂(Z)+P₃(Z) X + P₄(Z) X²1+aX+bX²+cX³}]barn atom^-1

where

$m$	$=$	$electron\; mass$
$X$	$=$	$\{Em\}$
$P$i(Z)	$=$	$D$i+ EiZ + FiZ2

The values of the parameters are put in the DATA statement within the routine GCOMPI. The fit was made over 511 data points chosen between:

The accuracy of the fit is estimated to be:

$\{\Delta \sigma \sigma \}=$

$\approx 10$	$for\; E$
$\le 5-6$	$for\; E$

$.$

PHYS221