Regular and Chaotic Motion Domains in the Channeling Electron's Phase Space and Mean Level Density for Its Transverse Motion Energy

TL;DR

This paper investigates the quantum energy level statistics of high-energy electrons and positrons in crystal channeling, revealing that Berry-Robnik distribution best describes the mixed regular and chaotic classical motion regimes.

Contribution

It provides a semiclassical analysis of energy level densities for electrons and positrons in channeling along [100], highlighting the applicability of Berry-Robnik distribution for mixed motion regimes.

Findings

Level spacing distribution fits Berry-Robnik better than Wigner or Poisson.

Classical motion can be both regular and chaotic at the same energy in [100] channeling.

Semiclassical energy level density computed for 10 GeV particles.

Abstract

The motion of charged particles in a crystal in the axial channeling regime can be both regular and chaotic. The chaos in quantum case manifests itself in the statistical properties of the energy levels set. These properties have been studied previously for the electrons channeling along [110] direction of the silicon crystal, in the case when the classical motion was completely chaotic. The case of channeling along [100] direction is of special interest because the classical motion here can be both regular and chaotic for the same energy depending on the initial conditions. The semiclassical energy level density (as well as its part that corresponds to the regular motion domains in the phase space) is computed for the 10 GeV channeling electrons and positrons. It is demonstrated that the level spacing distribution for both electrons and positrons can be better described by Berry--Robnik distribution than by both Wigner (completely chaotic case) or Poisson (completely regular case) distributions.