Effective charge and the mean charge of swift ions in solids

We perform a nonlinear study of the energy loss of light and heavy ions in solids using the quantum transport-cross-section method based on numerical solution of the Schrodinger equation. The charge of the ion—the relevant parameter in this calculation—is considered equal to the average ion charge measured after emergence from solid foils. When the calculated energy loss values are analyzed within the framework of the effective charge approach, the results of the present calculations are in excellent agreement with the empirical values and also show the expected scaling properties. Through this analysis, we find a relationship between the charge state inside the solid and the effective charge related to energy loss studies, which solves a seaming contradiction between these values. The implications of this study with respect to the Bohr-Lindhard and Betz-Grodzins models are discussed. DOI: 10.1103/PhysRevA.69.012902