Effect of removing the no-virtual-pair approximation on the correlation energy of the He isoelectronic sequence

The correlation energies (CEs) for the He-like ions are studied with the virtual-pair approximation (VPA) and with the no-virtual-pair approximation (NVPA). In contrast to the nonrelativistic CEs, the CEs calculated with relativity fell sharply as the nuclear charge Z increased, although the CE calculated with the NVPA was considerably lower than with the VPA for the heavier atoms. It is shown that CE calculated with a Hylleraas-type function implicitly includes the effects of the excitations into negative-energy states, which corresponds to the VPA. The present results verify that the strong dependence on Z of the CE of He-like ions is an essential effect of the relativity. (C) 2007 American Institute of Physics.