Quantum description of the positrons channeling near ⟨111⟩ direction of the silicon crystal

The fast charged particle's motion in the crystal under small angle to one of the crystallographic axes denselypacked with atoms can be described with high accuracy as the motion in the uniform potentials of the parallel atomic stringsthat conserves the particle's momentum component parallel to the string axis. The finite motion in the transverse plane in thiscase is called as the axial channeling. The quantum effects in the axial channeling can manifest inselves, first of all, as theenergy quantization for the motion in the transverse plane. This paper describes the numerical method for the transverseenergy levels and the corresponding wave functions for the positrons channeling in the ⟨111⟩ direction of the Silicon crystal.