Dynamic structure of electrons in Li metal: Inelastic synchrotron x-ray scattering results and interpretation beyond the random-phase approximation.

Abstract

The dynamic structure factor S(q,\ensuremath{\omega}) of electrons in Li-metal single crystals for q\ensuremath{\parallel}[100], q\ensuremath{\parallel}[110], and q\ensuremath{\parallel}[111] with 0.28 a.u. <q<1.4 a.u. was measured with 1-eV resolution by using inelastic scattering of synchrotron x radiation from DORIS II (Doppel-Ring Speicheranlage). Mainly for q>${q}_{c}$ (${q}_{c}$ is the plasmon cutoff vector) the fine structure of S(q,\ensuremath{\omega}) exhibits a strong dependence on the direction of the momentum transfer q. This crystal-lattice-induced peak structure is connected with minima of the combined density of states as due to band gaps across Bragg planes and can be interpreted as zone-boundary collective states within the limits of a two-band approximation. Comparison of the experimental results with model calculations of S(q,\ensuremath{\omega}), going beyond the random-phase approximation (RPA) by means of local-field corrections and also taking into account momentum-dependent lifetime effects for the inhomogeneous case (including band-structure effects) led to the following conclusions: (1) Most of the fine structure of S(q,\ensuremath{\omega}) is induced by the interaction of electrons with the ion lattice. (2) The overall shape of the S(q,\ensuremath{\omega}) spectra, mainly their strong deviation from corresponding homogeneous RPA results, is dominated by the momentum dependence of the inverse lifetime of quasiparticles with a steep rise at momentum ${p}_{0}$ which makes possible decay of quasiparticle states into a plasmon. (3) The influence of exchange and correlation on S(q,\ensuremath{\omega}) via a local-field correction factor is found to be appreciable.