On the analysis of Waterman׳s approach in the electrostatic case

•Applicability analysis of Waterman׳s approach is improved and discussed in detail.•The analysis is extended to the generalized point matching method.•The theoretical results obtained are tested using special calculations.

We reconsider (namely, conclusively improve, discuss in more detail, supply with more numerical tests, at last compare with the studies of other authors) and extend our earlier works on applicability of Waterman׳s approach. In the electrostatic case which is more simple but still principally similar to the light scattering one, we discuss the condition of existence of solution to the infinite system given by this approach and of convergence of solutions to the truncated systems with a growing number of equations. The condition found earlier and depending on the particle shape only (namely, all singularities of the analytic continuation of internal field must be more distant than all singularities of the analytic continuation of “scattered” field) must include the following correction for spheroids: the approach is applicable to any particles of this shape. We discuss how this condition can be related to other light scattering methods, in particular the generalized point matching one. As illustrations we present some results of special calculations made with high accuracy for inverse spheroids. Besides showing a general agreement of the theoretical applicability condition with numerical results and the works of other authors, we note several still unclear aspects of the problem.