Spectral distribution methods in effective interaction theory

Spectral distribution methods are used to suggest alternative forms for effective interaction calculation. Using the configuration centroid operator as the unperturbed Hamiltonian is found to yield a residual interaction with minimal Euclidean norm. If the effective interaction is expanded in terms of orthogonal polynomials appropriate to the configuration density, the leading term is more meaningful than those in existing series. Using the same technique of orthogonal polynomial expansion, the calculation of diagonal matrix elements of higher order terms in the perturbation expansions reduces to an evaluation of traces which are more easily calculable. Convergence of both polynomial expansions is tied to the convergence of the spectral density to normal form which itself is governed by a strong principle, the central limit theorem.