Wave functions of the transverse motion stationary states of the 5 and 20 gev positrons channeling in <111> direction of the silicon crystal

The fast charged particle's motion in the crystal under small angle to one of the crystallographic axes densely packed with atoms can be described with high accuracy as the motion in the uniform potentials of the parallel atomic strings that conserves the particle's momentum component parallel to the string axis. The finite motion in the transverse plane in this case is called the axial channeling and can be quantized. This paper presents the full catalogue of the transverse motion energy levels and the corresponding wave functions computed numerically for the positrons with energies of 5 and 20 GeV channeling in the <111> direction of the silicon crystal. The classification of these stationary states according to irreducible representations of the C3v group is given.