Band-structure-dependent collective states in simple metals

Anisotropic structures in the inelastic-scattering cross section of x rays from single-crystal Li and of fast electrons from single-crystal Na and Al are found to arise from zone-boundary collective states (ZBCS) that, in contrast to the classical plasmon, depend strongly on the symmetry and on the strength of the crystal potential. We show that within the random-phase approximation (RPA), a nearly-free-electron-like two-band model is able to describe these states existing for q along various high-symmetry directions of the crystal. In Li in particular, a 〈200〉 ZBCS appears as a continuation of the plasmon beyond the cutoff wave vector ${q}_{c}$. For many years structures in this (q,\ensuremath{\omega}) regime have been associated with correlation effects beyond the RPA. Furthermore, due to the high sensitivity on the crystal potential, measured ZBCS's yield valuable information on the band structure, which are currently intensively studied by angularly resolved photoemission.