Some remarks on the theory of the dielectric response of crystals and on the lorentz‐lorenz formula

An investigation is made of the macroscopic dielectric function of a model insulator including local field effects and treating exchange by (i) the many‐body perturbation technique, (ii) the mean field, and (iii) excitonic approximations. The different methods yield similar results, showing the reliability of approximations (ii) and (ii) in most cases. Also the validity of the Lorentz‐Lorenz formula is discussed, showing that it is always valid in cubic crystals, if the “atomic” polarizability is suitably defined as the limit of the crystal polarizability for vanishing dipole—dipole interaction.