The effect of relaxation of the lattice around the core hole on the soft X-ray spectra of metals near the Fermi edge, with particular application to Li and Na, is investigated. Neglecting lifetime effects, linearizing the core-hole phonon coupling and making a harmonic approximation for the phonons, the problem is exactly solvable by a generalization of a method previously proposed by Langreth to finite temperatures. Numerical calculations are carried out within the framework of linear response theory using the Thomas–Fermi, R.P.A., and Singwi et al. dielectric functions, and realistic phonon spectra obtained from neutron inelastic scattering data. The calculations give rise to lattice relaxation effects of similar magnitude in both metals. The results are considerably smaller than would be necessary to explain the shape of the Li spectra (contrary to a previous suggestion), while in Na the contribution is calculated to be of the same order of magnitude, but with a different temperature dependence, than the other factors influencing the shape of the absorption edge.
Selecting core-hole localization or delocalization in CS2 by photofragmentation dynamics