A 1/ Z expansion study of the 2s2p1P and 3P autoionizing resonances of the helium isoelectronic sequence

The calculation of approximate wave functions describing autoionizing resonances is formulated in terms of Hylleraas-Scherr-Knight 1/Z expansion perturbation theory. The optimization of a screening parameter is discussed and it is shown that erroneous results may be obtained if the screening parameter is improperly chosen. The solution is expanded in a finite, correlated basis set and results obtained for the 2s2p 1P and 3P resonances of the helium isoelectronic sequence. The 1/Z expansion method uniquely identifies which of the N roots arising from the diagonalization of the Hamiltonian in an N dimensional basis set corresponds to a particular autoionizing state.