Current-density functional theory of the friction of ions in an interacting electron gas.

Recently [1], the dynamical contribution to the friction coefficient of an electron gas for ions has been obtained quite generally in terms of the exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT). To implement this approach practically, an efficient approximation, like the local-density approximation (LDA), is needed for the dynamical xc kernel. It is, however, known that the {\em scalar} xc kernel of the TDDFT is a nonlocal quantity for which the LDA is not only inaccurate, but also contradictory [2]. Here we recast the theory into the terms of the {\em tensorial} xc kernel of the current-density functional theory [3] in which form the LDA can be applied. Our numerical results are in a considerably better agreement with the experimental stopping power of Al than it has been the case within the LDA to the TDDFT. [1] V.U.Nazarov {\it et al.}, Phys. Rev. B71, 121106 (2005). [2] G.Vignale, Phys. Lett. A209, 206 (1995). [3] G.Vignale and W.Kohn, Phys. Rev. Lett. 77, 2037 (1996).