One-electron and many-body effects in x-ray absorption and emission edges of Li, Na, Mg, and Al metals

A formalism is developed for the analysis of x-ray absorption and emission edges of simple metals in terms of one-electron and many-body effects. These include the transition density of states, the core-hole lifetime, the Franck-Condon lattice excitations, the Fermi function, the Mahan-Nozières-De Dominicis (MND) many-body response of the conduction electrons, the Onodera spin-orbit exchange, and the instrumental response function. Our formalism is applied to the available edge data from the metals Li, Na, Mg, and Al. The basic findings are that the Li $K$ edge is rounded by phonon excitations, the $L_{2,3}$ edges of Na, Mg, and Al are peaked primarily by the many-body effects, and the $K$ edges are rounded solely by the $1s$ hole lifetime. Transition-density-of-states structure makes a significant contribution only in the $L_{2,3}$ emission edges of Mg and Al, spin-orbit exchange only in the $L_{2,3}$ absorption edge of Na. Present theories do not account quantitatively for the minimal effect of many-body screening on the Li $K$ absorption edge because of direct exchange scattering. For A1 it is shown that a unique set of Friedel phase shifts accounts in detail for the x-ray photoemission (XPS) singularity index as well as for the many-body effects in the $K$ and $L_{2,3}$ emission and absorption edges. For Mg, the XPS and $L_{2,3}$ edge data predict a small positive $K$-edge exponent, while for Na a small negative one is predicted. Detailed comparisons with all known earlier experimental and theoretical work are made. The essential conclusion from this study is that irrespective of other factors, many-body effects make significant contributions to all the x-ray edges of the simple metals and that such effects are extremely well described by the MND theory.