Influence of correlations and of the core hole on metal x ray spectra

The emission and absorption spectra of simple metals are calculated taking into account many-body correlations in the electron gas. The calculations are performed up to first order in the RPA effective electron-electron interaction as well as in the RPA potential of the core hole. The first order theory of Longe and Glick has been reformulated to take account correctly of the normalization of the many-body `golden rule'. The divergency throughout the main band is eliminated and this new theory allows an estimate of the intensity of the Fermi edge singularity arising from the transient character of the core hole. The effect depends strongly on the structure of the electron wave functions close to the ion site. Strong cancellations of terms appear in the calculation of the intensity spectrum. This helps to explain why the bands are roughly one-electron like except for the low and high energy features. The calculations presented in this paper account qualitatively for most of the observed features which do not depend on band structure. Special application is made to the L emission and absorption spectra of sodium.