Density of states induced by a hydrogenic impurity in a metal

In this work, we present a parametrization of the density of states induced by a hydrogenic impurity in a metal that is described by a jellium. The parametrization has the most important features of the induced density of states (I-DOS). Among others, it includes the l=0 shallow doubly occupied bound state observed at low jellium densities when rs is higher than the binding value rs,B, and is consistent with the charge pile-up around the hydrogen due to the non-linear screening. It also addresses the infinite discontinuity in the l=0 I-DOS at the bottom of the band when rs exceeds rs,B. Our results compare well with other calculations, including more sophisticated ones that include spin-polarized and many-body calculations. Many applications may take advantage of the tractability of this parametrization, as a reference or for specific calculations.