Local-Field Corrections to Coulomb Interactions

Abstract

The effective charge-charge, charge-dipole, and dipole-dipole Coulomb interactions are calculated for a solid dielectric. The static dielectric screening of the solid is included by using the point-dipole model, which assumes that the host ions are polarizable points. This model allows the dielectric screening of Coulomb interactions to be included exactly, since the local-field corrections can be summed to all orders. The longrange charge-charge interactions are just screened by ${\ensuremath{\epsilon}}^{\ensuremath{-}1}$, where $\ensuremath{\epsilon}$ is the Lorentz-Lorentz dielectric function. The long-range interactions involving dipoles can be understood by assigning the dipoles an external moment ${\ensuremath{\mu}}_{e}=\frac{(\ensuremath{\epsilon}+2)\ensuremath{\mu}}{3}$, where $\ensuremath{\mu}$ is the moment in a vacuum. This form of the external moment applies only to dipoles in positions of cubic symmetry.