# Effective fields in cubic lattices with extended charges

## Abstract

The effective field in cubic lattices is calculated for a simple model in which the electrons have spatially extended charge distributions. For simple cubic, body-centered cubic, and face-centered cubic lattices in which the electrons in each primitive cell are infinitesimally displaced from rigid cores, the effective field can be written Eeff=E+(43)P, where E is the average electric field in the medium, and P is the polarization. The coefficient varies from zero for very extended electronic charge distributions to 1 for the limit of point charges. Values of for Gaussian distributions of intermediate width are given. Effective fields are also calculated for the rocksalt, zincblende, and cesium chloride structures. These results involve an additional coefficient which also varies between 0 and 1. For moderate overlaps between electronic charge distributions of next-nearest neighbors the effective fields differ appreciably from the Lorentz field E+(43)P. © 1964 The American Physical Society.