Energy loss of ions in solids: Non-linear calculations for slow and swift ions

Abstract

The historical approach to describe the energy loss of swift ions in solids is based on the Bohr, Bethe and Bloch theories. As is well known, the central parameter in these theories is the ratio η= Z 1 e 2/ℏ v, whose value is generally used to delimit the ranges of applicability of the Bohr ( η>1) and Bethe ( η<1) theories. The transition between these regimes can be obtained by changing the ratio Z 1/ v, although not by simply changing v. In fact, this scheme breaks down at low velocities, where quantum and non-linear effects arise. This domain is characterized by the strong oscillatory Z 1 dependence of the stopping powers. This paper proposes a self-consistent non-linear approach to calculate the energy loss of heavy ions on a wide range of velocities. The model is based on the transport cross-section approach and on a previous extension of the Friedel sum rule for moving ions. The purpose of this study is to develop a non-linear stopping power evaluation method that could be applied at finite ion velocities, bridging the current gap between the low- and high-energy models.