Dynamic structure of electrons in Be metal by inelastic x-ray scattering spectroscopy

The dynamic structure factor S(q,ω) of electrons in Be metal was measured with 1-eV resolution by means of inelastic scattering of synchrotron x radiation both on single crystals for a large number of different directions of q (among others, q∥${\mathrm{g}}_{100}$,${\mathrm{g}}_{110}$,${\mathrm{g}}_{101}$ ${\mathrm{g}}_{001}$) and on polycrystalline samples with 0.45 a.u.<q<1.69 a.u. The experimental results were compared with model calculations, which go beyond the random-phase approximation. The overall shape of experimental S(q,ω) can be understood when taking into account appropriately both state-dependent quasiparticle lifetime and local-field corrections. The strongly q-orientation-dependent fine structure of S(q,ω) can be interpreted as being due to excitation gaps, which are generated by transitions to final states on Bragg planes. This type of fine structure can be utilized to get information about the band structure in a very direct manner. There is every indication that also the less q-orientation-dependent fine structure found in experimental S(q,ω) is induced by ion-electron interaction, although another origin (electron-electron interaction) cannot be ruled out completely.