Gaussian Theory

Various conflicting forms have been proposed for Gaussian straggling functions, but most of these appear to have little theoretical or experimental basis. However, as noted by Schorr [] it has been demonstrated by Seltzer and Berger [] that for $\kappa \ge 10$

the Vavilov distribution can be replaced by a Gaussian of the form :

$f(\; \epsilon ,\; \delta s)\; \approx \{1\xi \{2\; \pi \kappa \}(\; 1\; -\; \beta 2/2\; )\}exp[\; \{(\; \epsilon -\epsilon )22\}\{\kappa \xi 2(1-\; \beta 2/2)\}]$

thus implying

$mean$	$=$	$\epsilon$
$\sigma 2$	$=$	$\{\xi 2\kappa \}(1-\beta 2/2)\; =\; \xi E$max(1-β2/2)