The relative error of calculations at the Pöschl-Teller model potential for the planar channeled muon

Abstract

In the framework of quantum mechanics, we investigate muon channeling in the Si (200) crystal. The transverse energy levels and wave functions are obtained for the Pöschl-Teller and the Doyle-Turner potentials. Comparative analysis demonstrates that analytical results of calculations obtained on the base of the Pöschl-Teller potential are in a good agreement with the numerical results of calculations in the Doyle-Turner model for the low energy levels. These results for the muon with rest mass m µ and relativistic factor γ are valid for any particle with elementary charge and rest mass m and relativistic factor γ m = γ(m µ /m). Therefore, our results can be useful for the preparation and performing the experimental investigation of the various phenomena accompanying particle channeling.