Theoretical resolution of theH−resonance spectrum up to then=4threshold. II. States of1Sand1Dsymmetries

Abstract

The resonance spectrum of ${\mathrm{H}}^{\ensuremath{-}}$ for ${}^{1}S$ and ${}^{1}D$ symmetries up to the $n=4$ threshold has been computed by solving the corresponding complex eigenvalue Schr\odinger equation in terms of basis functions of real and complex coordinates. These functions are chosen and optimized judiciously and systematically in order to account for the specific details of electronic structure, electron correlation, and multistate and multichannel couplings characterizing the problem. Large sets of Slater orbitals, extending in a regular manner to about 8000 atomic units, were employed in order to describe properly the full range and especially the large-$r$ behavior of the localized part of these resonances, as their energy approaches their corresponding threshold. Energies, widths, and wave-function characteristics are presented for $33{}^{1}S$ states and $37{}^{1}D$ states having widths down to about $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\mathrm{a}.\mathrm{u}.$ Of this total of 70 states, only 32 have been identified before via the application of different theoretical approaches, or, for very few of them, in scattering experiments. By adopting the Gailitis-Damburg model of dipole resonances as the relevant zero order model, we identify unperturbed and perturbed spectral series, in analogy with the well-known spectra of neutral atoms or positive ions, where the zero-order model is based on the Rydberg spectrum of the $1/r$ Coulomb potential. For perturbed spectra, only rough correspondence can be made with the smooth series predictions of the zero-order model. By achieving many-digit numerical precision for our results, we demonstrate the occasional presence of unique irregularities associated with each threshold, such as the existence of overlapping resonances and of ``loner'' resonances (i.e., not belonging to any series) below and above threshold. An example for the latter is a ${}^{1}D$ shape resonance above the $n=3$ threshold. This state was already identified by Ho and Bhatia [Phys. Rev. A 48, 3720 (1993)]. However, our values for the energy above threshold $(\ensuremath{\Delta}E=0.49497\mathrm{meV})$ and for the width $(\ensuremath{\Gamma}=8.632\mathrm{meV})$ differ significantly from theirs $(\ensuremath{\Delta}E=116.94\mathrm{meV}$ and $\ensuremath{\Gamma}=157\mathrm{meV}).$