Simplest doubly charged negative ion: Nonexistence ofH2−resonances

Two independent types of ab initio calculations for three electrons in the field of a proton have been carried out. Neither calculation shows any evidence for the existence of a resonant state of ${\mathrm{H}}^{2\mathrm{-}}$ contributing to e+${\mathrm{H}}^{\mathrm{-}}$ inelastic scattering, at energies above the three-electron escape threshold. One of the methods used is based on an eigenchannel R-matrix calculation carried out within a reaction volume of finite radius ${\mathit{r}}_0$, followed by an averaging procedure over ${\mathit{r}}_0$. A second method is based on a configuration-interaction study of the dependence of the 2${\mathit{s}}^2$2p ${}_{}{}^2{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ resonance on the nuclear charge Z. These calculations suggest that previous experimental and theoretical studies of this system were in erroneous agreement that two ${}_{}{}^2{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ resonances exist in ${\mathrm{H}}^{2\mathrm{-}}$ above the three-electron escape threshold. We also show that the earlier apparent agreement between experimental and theoretical resonance properties would violate unitarity of the collision matrix.