Retardation correction to the Lorentz-Lorenz formula for the refractive index of a disordered system of polarizable point dipoles

An approximate expression for the effective dielectric tensor of a fluid or suspension of spherical particles with a polarizable point dipole at the center is derived by a selection of terms in the cluster expansion. Full account is taken of the effect of retardation. The effective dielectric tensor depends on wave vector and frequency. In the limit of zero frequency the derived expression reduces to the wave-vector-dependent tensor found from electrostatics by the same procedure. In the limit of zero frequency and zero wave vector it reduces to the Clausius-Mossotti formula. The transverse part of the tensor may be regarded as a generalization of the well-known Lorentz-Lorenz formula for the refractive index. It is shown that the generalization leads to unphysical results if the damping of the individual spherical particles is too small. This implies that correlation corrections must be taken into account.