Energy-loss spectrum of swift ions in charge-state equilibrium

The energy-loss spectrum of ions in the presence of charge exchange is analyzed theoretically for large path lengths. The evaluation is based upon steepest-descent integration of the generalized Bothe-Landau formula. General approximation formulas for the spectrum are derived without reference to particular collision cross sections, and their regions of validity are discussed. The approximations are tested against numerical curves for 32-MeV He-3 ions in carbon. General asymptotic expressions for the peak energy loss and half-widths of the spectrum are found. The asymptotic expression for the mean-to-peak interval is specified and analyzed. In particular, it is shown and illustrated on a model system that the sign of the difference between the peak and mean energy loss may be opposite to that in the one-state case.