Hylleraas Variational Calculation of Auto-Ionization States

Positron attachment to the He(ns21Se) states

“…Both the configuration interaction (CI) [1] and SVM He(2s 2 1 S e ) energies lie about 10 −5 a.u. below the earlier Hylleraas calculation [2].…”

“…The projection method [2,3] provides an easy to implement method for the identification of resonances and determination of their positions. In this method, the target electrons are not allowed to occupy those low-lying states that could result in the autoionization of the system.…”

“…These calculations were performed using the same projection operator approach that was originally applied in some of the earliest calculations of the helium doubly excited spectrum [2,3]. The results identified a possible pathway for experimental confirmation that positrons can be attached to electrically neutral atoms to form bound states.…”

“…The structures of these resonances are initially analyzed using bound-state methods by using projection operators that prevent decay into an autoionizing continuum [2,3]. The complex rotation (CR) method is then used to estimate the widths of both resonances.…”

Sum-rules in resonance calculations with complex coordinates

“…In this paper some new calculations of autoionization resonances of the helium atom are presented in support of our earlier claim [51 that sum rules may serve as a viable means to assess the quality of a resonance calculation even if no data exist for comparison. For the purpose of this paper, examples are chosen for which very accurate calculations have been reported [6,7,8]. The correlated wavefunctions used in the present calculations are all chosen in the generator coordinate representation described in an earlier publication [9].…”