Title: An all-electron product-basis set: application to plasmon anisotropy in simple metals

Abstract: An efficient basis set for products of all-electron wave functions is proposed, which comprises plane waves defined over the entire unit cell and orbitals confined to small non-overlapping spheres. The size of the set and the basis functions are, in principle, independent of the computational parameters of the band structure method. The approach is implemented in the extended LAPW method, and its properties and accuracy are discussed. The method is applied to analyze the dielectric response of the simple metals Al, Na, Li, K, Rb, and Cs with a focus on the origin of the anisotropy of the plasmon dispersion in Al and Na. The anisotropy is traced to tiny structures of the one-particle excitation spectra of Al and Na, and relevant experimental observations are explained.