SELECTING ADEQUATE CAPACITY AND METHODS CALCULATION OF QUANTUM STATES OF AXIALLY CHANNELED ELECTRONS AT HIGH ENERGIES

The work examines the movement of relativistic particles (electrons) along close-packed chains of atoms in single crystals (axial channeling). The motion of electrons is considered in the accompanying reference frame (CFR), which itself moves with a speed equal to the longitudinal axis of the channeling and the velocity component of the channeled particle. In SSO, the motion of an axially channeled particle is two-dimensional (flat), and for electrons with energies up to several GeV it will be non-relativistic, as in the hydrogen atom. The quantum characteristics of motion are determined by the energy of the particle (it plays the role of the mass of the electron in a two-dimensional “atom”), as well as by the parameters of the average potential of the atomic chain, which depend on the crystallographic direction and chemical composition of the crystal. Axial channeling can be considered as a unique model of a relativistic two-dimensional atom with controlled parameters. The work shows that the main characteristics of quantum states of transverse motion of particles during axial channeling are weakly sensitive to the functional dependence of the parameters of the average potential on transverse coordinates. To calculate such characteristics, it is convenient to use Bohr’s approximate quantization method, which allows one to obtain the result analytically. The modified Bohr quantization method can be used to calculate the characteristics of transverse motion, which even goes beyond the nonrelativistic approximation even in SSO. In this work, the energy spectra of permissible states of transverse orbital motion are calculated for several variants of model axially symmetric potentials. It is shown that, despite differences in structure, the average distances between energy levels are slightly insensitive to the choice of potential model. The level energies were found both for the case when a nonrelativistic approximation is applicable to describe the transverse motion in the SSO, and in a situation that goes beyond the nonrelativistic approximation.

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