Geometrical optics method in the theory of channeling of high energy particles in crystals

TL;DR

This paper explores the application of geometrical optics to describe the scattering of high-energy charged particles in thin crystals, revealing effects like zero total scattering cross-section at specific thicknesses.

Contribution

It introduces a geometrical optics approach to particle channeling in crystals and identifies a Ramsauer-Townsend-like effect in ultrarelativistic particle scattering.

Findings

Total scattering cross-section depends on crystal thickness.

Existence of zero scattering cross-section at specific thicknesses.

Role of Morse-Maslov index in the wave function expression.

Abstract

The process of scattering of fast charged particles in thin crystals is considered in the transitional range of thicknesses, between those at which the channeling phenomenon is not developed and those at which it is realized. The possibility is shown of application of the methods of geometrical optics for description of the scattering process. The dependence is studied of the total scattering cross-section of ultrarelativistic positrons on target thickness in this range of crystal thicknesses. In the case of ultrarelativistic particles channeling the possibility is shown of the existence of an effect analogical to the Ramsauer-Townsend effect of conversion into zero of the total scattering cross-section at some values of crystal thickness. The important role is outlined of the Morse-Maslov index that enters into the wave function expression in the geometrical optics method.