Band structure effects on the plasmon dispersion in simple metals

The real part of the effective dielectric function is derived analytically in the pseudopotential approximation. For anyk-direction, the theory allows the evaluation of the plasmon dispersion, _p (k), which is found to be anisotropic in general due to band structure effects. Application of the theory to Al yields an isotropic shift atk=0 of _p (0) _v – 0.3 eV and explains the recently observed anisotropic behaviour of the dispersion very well fork < 0.6k _F .