Quantum Tunneling Effect on the Transverse Motion Energy Spectrum for the Channeling Positrons in the Silicon Crystal

The charged particles motion in the crystal could be either regular or chaotic. In the quantum picture the chaos manifests itself in the statistical properties of the energy levels set. The systems with regular motion domains in the phase space separated by the chaotic one are of a particular interest. The possibility to tunnel between dynamically isolated domains of the phase space influences essentially on the energy levels statistics. This effect account leads to Podolskiy–Narimanov distribution function. The tunneling matrix elements for the transversal motion of 20 and 40 GeV positrons axially channeled in [100] direction of Si crystal are estimated in the present paper. The parameter of the Podolskiy–Narimanov distribution is derived from this estimation. It is demonstrated that this distribution successfully describes the level spacing statistics for the energy levels set of the positron transversal motion.