PAuto-Ionization States of He andH−

Precision calculations of the energies of $P$ auto-ionization states of He and ${\mathrm{H}}^{-}$ are continued, and calculations of widths and shifts are initiated. The $P$-wave Hylleraas-type wave function of a previous calculation (Bhatia, Temkin, and Perkins) is augmented to include 56 terms, among them the most important powers of ${\mathcal{r}}_1$, ${\mathcal{r}}_2$, and ${\mathcal{r}}_{12}$ omitted in the previous calculation. The associated wave functions are then used to calculate shifts, widths, and $q$ values with exchange, exchange adiabatic, and polarized orbital wave functions representing the nonresonant continuum. It is found that the latter gives the most satisfactory agreement with experiment. Corrections for nearby resonances are also included. The variational calculation has been extended to include 84 terms for the ${}_{}{}^1{}_{}{}^{}P$ states of He. With inclusion of the shift, the positions of the first two resonances are within the experimental values of Madden and Codling; however, the lowest state is about 0.01 eV removed from the central value of the experiment. The mass-polarization correction is also discussed, but its value is far too small to reconcile the deviation from the mean.