Correction to the Moliere's formula for multiple scattering

TL;DR

This paper derives a quasiclassical correction to Moliere's multiple scattering formula, revealing that the correction depends on target density and thickness separately, which explains the formula's broad applicability.

Contribution

It introduces a new bulk density correction to Moliere's formula based on the first quasiclassical correction for arbitrary potentials.

Findings

The correction depends on density and thickness separately.

The correction is small even at high densities.

The result explains the wide applicability of Moliere's formula.

Abstract

The quasiclassical correction to the Moliere's formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to the Moliere's formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Moliere's formula.