The averaging along charged particle trajectories in a single crystal axial channeling

The charged particle moment distribution is determined on a single crystal axial channeling in single string approximation (SSA). A statistical Lindhard ensemble average for axial channeling is proved to be in SSA equivalent an averaging on the multitude of particle trajectories in continuous single string potential with the possible moment array. The computer simulation method of the state equilibrium functions calculation for axial channeling (energy loss, square growth of multiple scattering angle by thermal vibrating atomic nuclei etc.) is proposed