The Wannier two-electron ionisation ladder in many electron systems: the He1Podoubly excited states

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Abstract
The authors present a theory for the identification and accurate calculation of a particular class of double excited states which lead-as a function of excitation energy-to the 'Wannier state' at the two-electron ionisation threshold of any atom in any symmetry. The theory is more specific and uses suitably defined orthogonal MCHF zeroth-order wavefunctions which correspond to the state of lowest energy in each manifold defined by a particular symmetry in each shell. The choice of the zeroth-order wavefunction is systematic and allows for the self-consistent computation of the most important angular and radial (i.e. beyond the hydrogenic Hamiltonian) correlations. The remaining electron correlation is added variationally subject to specific orthogonality constraints. Their first application is to the He 1Po Wannier two-electron ionisation ladder (TEIL). They present conditional probability density plots of these states which show how the localisation around (r1)=(r2) and ( theta 12)= pi increases as function of the principal quantum number n (the authors went up to n=10). As the excitation energy increases, the significance of the radial correlation beyond that included in the MCHF zeroth-order vector is reduced to negligible levels. The predicted energies and corresponding oscillator strengths should be observable in a photoabsorption experiment. The energies are fitted to an effective Rydberg-like formula En=-(Z- sigma )2/(n+ mu )2 with sigma =0.16244 and mu =0.1595. It is hoped that when numerical accuracy permits it, the appropriate extrapolation of the two-electron photoexcitation cross section to threshold will allow the derivation of a reliable two-electron ionisation law.