Calculations of the screening of the charge of a proton migrating in a metal

The amount of screening of a proton in a metal, migrating under the influence of an applied electric field, is calculated using different theoretical formulations. First the lowest order screening expression derived by Sham [Phys. Rev. B 12, 3142 (1975)] is evaluated. Contrary to Sham, who estimates the screening to be negligible, we find a finite screening of the order of 15%. In addition, exact expressions are evaluated which were derived according to different approaches. For a proton in a metal modeled as a jellium the screening appears to be 15 +/- 10%, which is neither negligible nor reconcilable with the controversial full-screening point of view of Bosvieux and Friedel [J. Phys. Chem. Solids 23, 123 (1962)]. In reconsidering the theory of electromigration, a new simplified linear-response expression for the driving force is shown to lead to essentially the same result as found by Sorbello [Phys. Rev. B 31, 798 (1985)], who has used a rather complicated technique. The expressions allow for a reduction such that only the scattering phase shifts of the migrating impurity are required. Finally it is shown that the starting formula for the driving force of Bosvieux and Friedel leads exactly to the zero-temperature limit of well-established linear response descriptions.