Use of the virial theorem in the calculation of wavefunctions for helium autoionising states

Abstract

The virial theorem is used as a supplementary constraint, in conjunction with a normal variational principal, in order to obtain wavefunctions for the (2s2)1S, (2p2)1S, (2p2)1D, (2s, 2p)1P and (2s,2p)3P autoionising states of helium. Good energies are obtained, except for the 1D state. The angular-correlation properties of the wavefunctions are compared with those of Lipsky-Conneely type functions (1977) and the effect of the mixing of the s2 and p2 configurations in investigated for the 1S states. A comparison is made of the resonance widths calculated using various approximations for the degenerate continua and matrix elements of either the Hamiltonian H or the operator (PHQ+QHP). A compact and relatively simple expansion basis is used in order to simplify subsequent collision calculations. This does not allow mixing with higher autoionising states to be taken into account; this affects the correlation properties of the 1P and 3P states and the width of the (2p2)1S state.