Band-structure approach to the x-ray spectra of metals

A formalism to compute x-ray spectra due to core excitations in metals by using single-particle band-structure techniques is presented and illustrated with a detailed calculation of the $K,L$, and $M$ emission and absorption spectra of palladium over 200 eV. Within the muffin-tin approximation for the potential, any spectrum can be factorized into atomiclike and solid-state contributions. The atomiclike factor is the dipole transition strength connecting a core state to a muffin-tin orbital in a free-electron metal. The solid-state factor is proportional to the density of band states with angular momentum determined by the orbital symmetry of the core state and the dipole selection rules. These projected densities of states have been calculated by using a linearized version of the augmented-plane-wave method specifically designed to cover large energy ranges. In particular, the method can describe simultaneously several principal quantum numbers of the eigenstates (e.g., $4d$ and $5d$ for palladium).