Phonon effects on deep-level excitations in metals: Beyond the linear-screening and linear-coupling models

New theoretical developments in impurity lattice dynamics are presented, with the emphasis on phonon broadening of core levels in metals. Detailed calculations have been made for Li and Na. The effects of non-linear screening are evaluated for the first time and are shown to increase the phonon broadening by about 70% for Li compared with the linear-screening value. The present a priori estimate of the phonon broadening of the Li 1s level is the first which agrees with experiment. The effects of core-hole-lattice couplings of second order in ion displacements are also evaluated and shown to be unimportant for Li and Na. The usual linear-screening theory for lattice dynamics and for impurity-lattice couplings is analysed critically with regard to its sensitivity to the approximations for the pseudopotential and for the screening function. Both optimised model potentials and norm-conserving a priori potentials are considered. Finally, an indirect phonon broadening mechanism proposed previously is analysed and shown to give a negligible effect