  The motion of charged particles in a crystal in the axial channeling regime
can be both regular and chaotic. The chaos in quantum case manifests itself in
the statistical properties of the energy levels set. These properties have been
studied previously for the electrons channeling along [110] direction of the
silicon crystal, in the case when the classical motion was completely chaotic,
as well as for the ones channeling along [100] direction, when the classical
motion can be both regular and chaotic for the same energy depending on the
initial conditions. Here we study the positrons channeling in [100] direction.
This case is of special interest due to the substantial tunneling probability
between dynamically isolated regular motion domains in the phase space. The
interaction of the energy levels via tunneling distinctly changes the level
spacing statistics. All transverse motion energy levels as well as
corresponding stationary wave functions are computed numerically for the 30 GeV
positrons channeling in [100] direction of the silicon crystal. The values of
the matrix elements for the tunnel transitions are extractad from these data.
These results confirm the chaos assistance for the tunneling and the level
splitting. These values will be used in the further researches of the quantum
chaos manifestations in the channeling phenomenon.
