Soft X-Ray Emission in Metals

A general quantum-mechanical many-body treatment of soft x-ray emission in metals is presented. By considering the initial state of the system to be created by removing an electron from the ground state of an $N$-electron system, the energy-dependent emission intensity is related to a suitable contraction of the three-particle Green's function based on the $N$-particle ground state. While the formalism includes fully all electron-electron interactions, the main concern in this paper is with the effect of the x-ray vacancy on the surrounding electron gas. This is accounted for partially by summing a selected set of ladder graphs describing the repeated scatterings of an incident conduction electron on the vacancy. The formula for the intensity obtained in this way is similar to that for noninteracting particles except that a correlated wave function for the electron-hole pair replaces the usual product of two independent-particle wave functions. In the limit when the initial vacancy is assumed to act as a fixed heavy impurity center, our expressions reduce correctly to the square of a dipole-moment matrix element between the vacancy wave function and that for a conduction electron in the Hartree field of the impurity.