Theoretical resolution of theH−resonance spectrum up to then=5 threshold: States of3Posymmetry

Abstract

The spectrum of resonance states of ${\mathrm{H}}^{\ensuremath{-}}$ of ${}^{3}{P}^{o}$ symmetry up to the $n=5$ Hydrogen threshold has been resolved by identifying all the complex eigenvalues of the corresponding Schr\"odinger equation with widths down to about ${10}^{\ensuremath{-}9}$ a.u. In order to achieve this spectral resolution inside the continuous spectrum, we employed the previously described polyelectronic complex-eigenvalue Schr\"odinger-equation theory, with special choices of large trial two-electron spaces, constructed in terms of real and complex one-electron Slater-type orbitals. Electron correlation and multistate and multichannel couplings characteristic to the problem were accounted for with high numerical accuracy. The basis set of real orbitals constituting the localized part of the resonances, were chosen systematically so as to cover in a regular manner the configuration space from 3 a.u. up to about ${10}^{4}$ a.u. In this way, both the inner and the outer (very diffuse) orbitals as well as the possible cases of medium-range intrashell states were represented reliably. Energies, widths, and wave-function characteristics were computed and analyzed for 83 resonances below the $n=2,$ 3, 4, and 5 Hydrogen levels. The essence of these results is presented numerically as well as in special figures, whose purpose is to demonstrate the degree to which these complex eigenvalues fall into series according to the Gailitis-Damburg theory of dipole resonances. The existence of series of dipole resonances with characteristic energy and width scaling is used as the zero-order reference model. We found that, in general, the resonances indeed follow the regularity predicted by the Gailitis-Damburg model. At the same time, there are a few irregularities, caused by interseries perturbations. They appear especially strongly in regions where overlapping resonances exist. Using our previous results for the resonance spectrum of ${}^{1}{P}^{o}$ symmetry, similarities and differences are discussed. Finally, the existence of a shape resonance lying above the $n=3$ threshold, which has been predicted in earlier work, is confirmed. On the contrary, our calculations did not confirm the appearance of a shape resonance above the $n=2$ threshold, which has also been predicted before in the literature.