Calculation ofn=3intrashell resonance states ofHe−and of isoelectronic atoms

Abstract

We discuss the theory and computation of the lowest three, $n=3$ intrashell triply excited resonance states of ${\mathrm{He}}^{\ensuremath{-}}$ of Li, and of positive ions of the sequence, up to ${\mathrm{N}}^{4+}.$ These are the ${3s}^{2}3p{}^{2}{P}^{o},$ ${3s3p}^{2}{}^{4}P,$ and ${3s3p}^{2}{}^{2}D$ states, for which wave function characteristics, energies, and widths are reported. Contrary to recently published results for ${\mathrm{He}}^{\ensuremath{-}}$ and to earlier ones for ${\mathrm{N}}^{4+},$ we found that electron correlation and orthogonality to lower states are such that they make the ${}^{2}{P}^{o}$ state the lowest $n=3$ triply excited state (TES), as is the case with the $n=2$ shell. Our predictions for these states of ${\mathrm{He}}^{\ensuremath{-}}$ are in harmony with the measurements of Roy [Phys. Rev. Lett. 38, 1062 (1977)], which were interpreted only recently [C. A. Nicolaides and N. A. Piangos, J. Phys. B 34, 99 (2001)]. In addition, our value for the position of the Li ${3s}^{2}3p{}^{2}{P}^{o}$ TES, 175.15 eV, agrees with the measurement $(175.165\ifmmode\pm\else\textpm\fi{}0.050\mathrm{eV})$ of Diehl et al. [Phys. Rev. A 56, R1071 (1997)]. Apart from specifics, the paper discusses or points to certain basic aspects of computational quantum mechanics of such multiply excited states. For example, it refers to the utility of open-channel-like configurations toward proper convergence to a local energy minimum in the continuous spectrum, where quasibound and unbound states of the same symmetry lie below, and for which the normal eigenvalue properties of the discrete spectrum do not apply. Also, we discuss the possibility that is given by the state-specific theory for carrying out economic and physically transparent calculations and for deducing semiquantitative conclusions about the interplay between electronic structure, interference, and autoionization widths.