Quantum-Mechanical Description of Spin-1/2 Particles and Nuclei Channeled in Bent Crystals

TL;DR

This paper develops a comprehensive quantum-mechanical framework for describing spin-1/2 particles and nuclei channeled in bent crystals using cylindrical coordinates, including their anomalous magnetic moments and classical limits.

Contribution

It introduces a detailed quantum-mechanical model incorporating anomalous moments and transforms it into the Foldy-Wouthuysen representation for particles in bent crystals.

Findings

Derived Dirac equation with anomalous moments in cylindrical coordinates

Formulated quantum equations of motion for particles and spins

Clarified classical limits and physical interpretation

Abstract

General quantum-mechanical description of relativistic particles and nuclei with spin 1/2 channeled in bent crystals is performed with the use of the cylindrical coordinate system. The previously derived Dirac equation in this system is added by terms characterizing anomalous magnetic and electric dipole moments. A transformation to the Foldy-Wouthuysen representation, a derivation of the quantum-mechanical equations of motion for particles and their spins, and a determination of classical limit of these equations are fulfilled in the general case. A physical nature of main peculiarities of description of particles and nuclei in the cylindrical coordinate system is ascertained.