State-specific approach and computation of resonance states: Identification and properties of the lowest P-2(o) and D-2 triply excited states of He- - art. no. 052505

We discuss aspects of the theory and computation of resonance (autoionizing ) states of polyelectronic atoms and their positive and negative ions, in t he context of the state-specific approach, using as paradigms the He(-)2s(2 )2p P-2(o) and 2s2p(2) D-2 triply excited states. The He- D-2 resonance has been the subject of controversy about its nature and its very existence, w ith ramifications as to the physics of electron-He scattering measurements and as to the theory of resonance states in multiparticle systems in genera l. By carrying out a series of computations, we show how (quasi) localizati on of these resonances takes place. The results confirm the existence of th e D-2 resonance just below the energy of the He 2s2p P-3(o) resonance. with which it overlaps. The localization of the two He- resonances is achieved already at the single-configuration level, provided the orbitals are calcul ated by solving state-specific restricted Hartree-Fock (HF) equations. Acco unting for orbital flexibility and relaxation due to the self-consistent in teractions is essential to the achievement of a local energy minimum. The l ocalized nature of the wavepacket is revealed even more definitely by solvi ng appropriate multiconfigurational HF (MCHF) equations containing the info rmation from the self-consistent interaction with closed channels as well a s with the neighboring significant open ones. Reaching a reliable MCHF solu tion for a variety of polyelectronic multiply excited states may often be d ifficult, but once it is achieved it provides the overwhelmingly dominant c haracteristics of the state. It is then used as the reference wave function for computing variationally the remaining of the localized electron correl ation in terms of optimized analytic orbitals representing very nearly the full space of the electron virtual excitations. The calculation of the loca lized part Psi (0) and of E-0= < Psi (0)/H/Psi (0)>, is done by nonorthonor mal configuration interaction (NONCI) since parts of Psi (0) are optimized separately in terms of their own basis sets. The final Psi (0)s for the two resonances consisted of 683 symmetry-adapted configurations for the P-2(o) state and 778 ones for the D-2 state. Using these functions and final stat e scattering functions with continuum orbitals obtained numerically in term -dependent core potentials, without and with polarization, of a number of l ower-lying open channels, we employed the independent channel approximation and computed partial and total energy shifts and widths, the latter from e nergy-dependent golden rule expressions. Critical comparison of our results for E= E-0 + Delta, where Delta is the shift induced by the interaction of Psi (0) with the continuum, and for the width, Gamma, with the existing fe w experimental and theoretical values, led us to the conclusion that the E and Gamma lie in the following ranges: For the P-2(o) state: E=57.204 +/-0. 005 eV, Gamma =68-74 meV, and for the D-2 state: E=58.295 +/-0.010 eV. Gamm a = 38-55 meV. Of special theoretical and experimental interest is the dete rmination of the partial and total widths of the three-electron He- D-2 res onance, since it overlaps from below the two-electron threshold state He 2s 2p (3)p(o) whose position is at 58.312 eV with a width of 8 meV.