On spectral method in the axial channeling theory

TL;DR

This paper applies a spectral method to analyze the quantized transverse energy levels of electrons in axial channeling within crystals, demonstrating high resolution and potential for studying quantum chaos.

Contribution

It introduces a high-resolution spectral method for calculating energy levels of electrons in axial channeling, applicable to systems with many levels and relevant for quantum chaos research.

Findings

Energy levels for electrons in axial channeling are calculated for tens of MeV energies.

The spectral method achieves high resolution in energy level determination.

The method is suitable for investigating quantum chaos in crystal channeling.

Abstract

The quantization of the transverse motion energy in the continuous potentials of atomic strings and planes can take place under passage of fast charged particles through crystals. The energy levels for electron moving in axial channeling regime in a system of parallel atomic strings (for instance, [110] strings of a silicon crystal) are found in this work for the electron energy of order of several tens of MeV, when a total number of energy levels becomes large (up to several hundreds). High resolution of the spectral method used for energy level search has been demonstrated. Hence this method could be useful for investigation of quantum chaos problem.