Energy-loss spectra of light relativistic ions

The energy-loss spectrum of a light ion penetrating through a layer of material has been evaluated theoretically for a wide range of thicknesses. A low-thickness approximation represents an extension into the relativistic regime of a recent scheme which, in turn, represents an extension of Landau’s well-known formula. A high-thickness approximation represents an extension into the relativistic regime of results derived previously by means of the method of steepest descent. Taken together, the two approaches accurately bridge the gap between the Landau and the Gaussian regime, as is demonstrated by comparison with numerical evaluations of the comprehensive Bothe–Landau formula. Explicit results are given for peak energy loss and halfwidths dependent on target thickness and beam velocity in scaling variables producing slowly varying functional relationships.