Electromigration Force on a Proton with a Bound State

Abstract

The driving force on an ion in a metal due to an applied electric field, called the electromigration force, is built up out of two contributions, a wind force and a direct force. The wind force is due to the scattering of the current carrying electrons off the ion. The direct force works on the effective charge of the ion. In the present work we concentrate on the direct force on a migrating proton embedded in an electron gas. For this force a sign change is obtained as soon as a bound state is formed. In recent calculations hardly a sign change was seen, although a bound state was found in a self-consistent-potential for lower electron densities. Here we show that a supplementary term shows up, as soon as one accounts for the bound state explicitly. By this the problem has been solved regarding a possible lack of completeness of the published formalism. The results presented are based on square-well model potentials. By using different depths it is possible to show results for potentials without a bound state and accommodating one bound state.