Path Length Correction

A path length correction may be applied in an approximate manner. We have from the Fermi-Eyges theory [] $t\; =\; S\; +\; \{12\}\int$₀^tθ²(t)&sp;dt

where

$\theta$2(t)	$the\; mean\; square\; angle\; of\; scattering;$
$S$	$step\; size\; along\; a\; straight\; line;$
$t$	$actual\; path\; length.$

We have further: $\theta$²(t)= ( 0.0212 {Z_incpβ})²{tX₀}

$X$₀ is the radiation length. From () and () we get $S\; =\; t\; -\; K\; t$²withK = 1.12 x10^-4&sp;{Z_inc²p²β²X₀}

Equation () may be used to make the path length correction. Solving equation () with respect to t implies that, in order to obtain real solutions: ₀p²β²Z_inc²}

This condition provides an additional constraint to the maximum step length for multiple scattering (variable TMXCOR in routine GMULOF). The corrected step can be approximated as:

$t\; \approx S(1\; +\; KS)\; =\; S\; (\; 1\; +\; CORR)$

where CORR $\le 0.25$ due to condition ().

F.Carminati

PHYS328