Structure of below-barrier and above-barrier energy bands and wave functions of a particle in the periodic potential of crystalline lattice

Abstract

Structure of below-barrier and above-barrier energy bands and wave functions of a particle in the periodic potential of crystalline lattice Abstract. The knowledge of energy spectrum structure allows us to find the Bloch state wave functions. During the interaction of charged particles moving in a crystal, the wave functions represent the superposition of Bloch functions. The population of every Bloch state is characterized by Fourier-component squared. The analytical results received in the given work for periodic potential of a crystal lattice in the model of modified Pöschl-Teller's potential make a basis for studying the phenomena in a channeling mode of particles in crystals (the behaviour of particles at different depths of penetration into crystal, angular distributions of particles, both inside the crystal, and at its exited, etc.). The account of the zone structure of energetic spectrum of channeled electrons results in qualitative change of angular distributions of X-ray radiation under the Bragg angles. Therefore it is interesting within the framework of our approach to study the radiation, as well as an output of the nuclear reactions appearing in case of interaction of charged particles moving in a crystal.