Electron correlation for helium-like atoms

A recently proposed analytical approach to the ground-state energy of helium atom is generalised to study the effect of electron-electron correlation on the properties of helium isoelectronic sequence. The expectation values of the Hamiltonian and some important functions of radial distances are expressed in terms of derivatives of Lewis integrals which not only permit the straightforward variational calculation to get numerical results but also help one derive interesting recurrence relations for radial expectation values. The results presented for atoms from H- to Si12+ indicate that the present analytical model will have quantitative applicability for the study of electronic correlation in high-Z helium-like atoms within the framework of non-relativistic quantum mechanics. (orig.)