DAutoionization States of He andH−

Positions of the lowest ${}_{}{}^{1,3}{}_{}{}^{}D_{}^e{}_{}{}^{}$ autonization states of He and ${\mathrm{H}}^{-}$ below the $n=2\mathrm{}$ level of ${\mathrm{He}}^{+}$ and H have been calculated variationally using Feshbach's $Q$-operator formalism. The trial wave function is of the Hylleraas type with appropriate angular momentum factors. The widths and the shifts of the states have also been calculated. The shifts are found to be positive for all the states calculated here. The results with 112 terms for most states are lower than any previously calculated. The calculated lowest autoionization states of He and ${\mathrm{H}}^{-}$ (relative to the ground states of He and H, respectively) are 59.902 and 10.1185 eV, in good agreement with the observed values of 59.9 and 10.13 ± 0.015 eV.