Different Screening Constants for Different Physical Properties. I

Abstract

Expectation values of properties other than energy are calculated for the ground state of the two‐electron atom with arbitrary nuclear charge. The calculations are designed to test the use of simple wavefunctions with embedded screening constants, where different screening constants are used for different properties. The results are compared with the perturbation expansion of Scherr and Knight, who have determined a large number of properties correct through sixth order. Dalgarno has suggested that a screening constant be chosen so as to make the first‐order perturbation correction vanish for the property under consideration. Robinson has shown that this choice is equivalent to the requirement that the zeroth‐order wavefunction satisfy a hypervirial relation, where the hypervirial generator is related to the property through a differential equation. This procedure gives excellent numerical results for properties having positive definite operators. For the particular examples considered here (but not generally), Dalgarno's method gives expectation values which are too small. When applicable, slight improvements are obtained by maximizing the expectation value calculated with the zeroth and first‐order wavefunctions.