Asymptotic Theory of Channeling in the Field of an Atomic Chain and an Atomic Plane

TL;DR

This paper develops a rigorous asymptotic theory for diffraction scattering from extended atomic structures, revealing how particle densities vary with potential strength and incidence angles.

Contribution

It introduces a multiple asymptotic expansion method for solving the wave function integral equation in the context of atomic channeling.

Findings

Positively charged particle density on the chain axis is always below unity.

Negatively charged particle density can exceed unity at certain potential strengths.

The theory's validity conditions are explicitly derived.

Abstract

A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the problem, which are the range of the potential and the momentum components of the incident particle. For small angles of incidence the density of positively charged particles on the axis of a chain is always lower than unit y and the density of negatively charged particles has a maximum for certain strength of the potential which can exceed considerably unity. The conditions of validity of the proposed approach are obtained.