In this paper we study a certain class of generalized perturbation problem for the isotropic three dimensional harmonic oscillator, forl=0 states only, for all excited states. The efficacy of our formalism is tested by studying the Killingbeck potential in detail. We also briefly present our results using the diagonal Padé approximants.

The occurrence of discontinuities in the energy spectrum of thes-wave Hamiltonian in three dimensionsH(μ, λ) =p²/2 − 1/r + 2µr + 2λ²r² has been reported by us. In this communication we develop a unified understanding, based principally on the topography of the energy surfaces, of the different discontinuities we reported earlier. These discontinuities do not in general occur wherever the corresponding classical system would display catastrophic behaviour.

Rescaled mean spherical approximation (RMSA) has been used to calculate the structure factor for the aqueous suspension of polystyrene macroions with the interaction potential taken according to Derjaguin and Landau (1941) and Verwey and Overbeek (1948) (DLVO) model. The effects of charge over the macroion and size on the surface potential and therefore, the structure factor have been studied. The breakdown of the DLVO potential with an excess charge over the macroion (⩾800e) has been reported. The oscillation in the first peak height of structure factor versus wave vector curve with size has been correlated with the Debye length.

An efficient fast Fourier transform method has been employed to determine correlation function [g(r*)] using the structure factor [S(Q*)] calculated with the rescaled mean spherical approximation (RMSA) and the DLVO potential. Based on this function a parametric (size and charge) study of the ordering in a highly charged and concentrated macroions (an ideal colloid) has been made. The strength of the correlation increases with the increase in the charge on macroions and it saturates after acertain value. Similarly, a critical diameter of the particle depending on the charge on it has been found at which normal feature of the ordering disappears.