The amount of screening of a proton in a metal, migrating under the influence of an applied electric field, was calculated using various theoretical formulations. Firstly, the lowest-order screening expression derived by Sham was evaluated. Contrary to this, which considered the screening to be negligible, a finite screening was found which was of the order of 15%. So-called exact expressions were evaluated which were derived using other approaches. For a proton in a metal modeled as jellium, the screening appeared to be 15%; which was neither negligible nor consistent with the controversial full-screening Bosvieux-Friedel point-of-view. In reconsidering the theory of electromigration, a new simplified linear-response expression for the driving force was shown to lead to essentially the same result as found by Sorbello, who had used a relatively complicated technique. The expressions permitted a reduction such that only the scattering phase-shifts of the migrating impurity were required. Finally, it was shown that the starting formula for the Bosvieux-Friedel driving force led exactly to the zero-temperature limit of well-established linear response descriptions.

Calculations of the Screening of the Charge of a Proton Migrating in a Metal. A.Lodder: Physical Review B, 2006, 74[4], 045111 (11pp)