Dynamics of the most probable energy loss by relativistic ions

Simple but very general formulas determining the parameters of the statistical distribution of inelastic energy losses (in particular, their most probable values) by relativistic ions as functions of the velocity and path length in a substance have been derived on the basis of the generalization of the classical Landau approach and steepest descent method. These expressions are more accurate than the well-known formulas and significantly expand the domains of applicability of the latter. Comparison with the numerical results confirms the high accuracy of the resulting analytical representations in wide intervals of the parameters and reveals their limitation.