Selection of an Adequate Interaction Potential to Describe Planar Channeling of Relativistic Particles

Abstract

This work considers planar channeling of relativistic particles in a comoving frame of reference moving at a speed equal to the longitudinal component of the velocity of the channeled particle. In SSO, the motion of a particle during planar channeling will be one dimensional, and for electrons and positrons with energies up to several gigaelectron volt, it will be nonrelativistic, as in the hydrogen atom. potential from transverse coordinates. To determine the main characteristics of such a movement, it is proposed to use approximate Bohr–Sommerfeld quantization methods, which make it possible to make such a calculation analytically. The approximate method for calculating quantum states can be extended to consider transverse motion beyond the nonrelativistic approximation, even in a comoving frame. The energy distributions of permissible states of transverse finite motion are found for several variants of model potentials. It is shown that, despite the difference in the structure of energy levels, the average distances between energy levels are practically insensitive to the choice of model potential. The energies of the transverse motion levels are found for the case where the nonrelativistic approximation is not applicable even in the comoving reference frame.