Construction of the Rayleigh Approximation for Axisymmetric Multilayered Particles, Making Use of Eigenfunctions of the Laplace Operator

Abstract

The Rayleigh approximation is constructed from the solution of the electrostatic problem for axisymmetric multilayered particles. The approach used is based on the consideration of surface integral equations analogous to those applied in the extended boundary condition method (EBCM) for solving electromagnetic problems. The electric fields are connected with scalar potentials, which are represented by their expansions in terms of eigenfunctions of the Laplace operator written in spheroidal and spherical coordinates. The unknown expansion coefficients are derived from infinite linear algebraic equations. The explicit solution found in spheroidal coordinates for multilayered spheroids coincides with known solutions for homogeneous and core-mantle particles. Bibliography: 17 titles.