Stopping of ions based on semiclassical phase shifts

We develop a semiclassical theory of the stopping of ions in matter, aiming at a wide validity range in terms of ion energies and mass number. The excitation of a target electron is described as a binary ion-electron interaction governed by a screened-Coulomb potential. The energy loss is expressed in terms of the transport cross section for electron-ion scattering which is calculated in a semiclassical approximation to the scattering phase shifts. Exact numerical integrations of the Schroedinger equation are used for quantitative tests of the derived results. This approach provides a nonperturbative representation of the energy loss which bridges the gap between classical and quantal descriptions. It applies to nonrelativistic velocities for light and heavy ions with arbitrary charge states, and it reproduces typical quantum phenomena such as the oscillatory atomic-number dependence of stopping cross sections at low energies. Calculated results have been compared with predictions from linear and nonlinear stopping theory, in particular for stopping in the electron gas and by a quantum harmonic oscillator. Moreover, attention has been paid to the Bloch correction which, in the present scheme, approaches Bloch's well-known expression but does not blow up at low projectile speed. We have also determined a generalized Blochmore » correction which depends on the ion charge. Particular attention has been given to the description of static and dynamic screening of a dressed ion.« less