Refractive Index, Attenuation, Dielectric Constant, and Permeability for Waves in a Polarizable Medium

Abstract

A new method is presented for calculating the refractive index, attenuation, dielectric constant, and permeability for electromagnetic waves in a medium of polarizable particles. It is similar to the method of Yvon and Kirkwood for finding the static dielectric constant. The main merit of the method is that it avoids the statistical hypotheses used in such calculations by Lorentz, Reiche, Hoek, Rosenfeld, and other authors. In addition, it permits the calculations to be continued to any degree of accuracy. We first use the method to obtain the dispersion equation as a power series in the molecular polarizability. The nth term in this series involves the distribution function of n + 1 particles. The terms of first and second degree are written out explicitly in terms of the two‐ and three‐particle distribution functions. When terms of second and higher degree are omitted and the result specialized to particles with a scalar electric polarizability and zero magnetic polarizability, the dispersion equation agrees with that of Rosenfeld. When terms of second degree are retained and the static limit considered, the result reduces to that of Yvon. We next use the method to obtain the dispersion equation as a power series in the particle number density, which seems to be new. To obtain it we introduce ``pure'' n‐particle scattering functions, which are analogous to the Ursell functions of statistical mechanics. This permits us to obtain the density expansion directly in a form simpler than is obtained by resumming the polarizability series.