<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-electron contribution to the stopping power of transition metals

We present a nonperturbative model to describe the stopping power by ionization of the $d$ electrons of transition metals. These metals are characterized by the filling of the $d$ subshell and the promotion of some of the electrons to the conduction band. The contribution of $d$ electrons at low-impact energies has been noted experimentally in the past as a break of the linear dependence of the stopping power with the ion velocity. In this paper we describe the response of these electrons considering the atomic inhomogeneous momentum distribution. We focus on the transition metals of groups 10 and 11 in the Periodic Table: Ni, Pd, Pt, Cu, Ag, and Au. Results are shown to describe the low-energy stopping power, with good agreement with the experimental data and available time-dependent density-functional theory results. By combining the present nonperturbative model for the $d$-subshell contribution with other approaches for the valence electrons and for the inner shells, we provide a coherent theoretical method capable of describing the stopping power of these transition metals from the very-low- to the high-energy region.