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

The dynamic structure factor S(q,ω) of electrons in Li-metal single crystals for q∥[100], q∥[110], and q∥[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,ω) 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,ω), 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,ω) is induced by the interaction of electrons with the ion lattice. (2) The overall shape of the S(q,ω) 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,ω) via a local-field correction factor is found to be appreciable.