Comparison of doubly-excited helium energy levels, isoelectronic series, autoionization lifetimes, and group-theoretical configuration-mixing predictions with large-configuration-interaction calculations and experimental spectra

For comparison with our recent group-theoretical predictions of configuration-mixing coefficients, we report extensive configuration-interaction calculations for doubly excited states in the helium isoelectronic sequence below the $N=2\mathrm{}$ ($S, P, D$ states), $N=3\mathrm{}$ ($S, P, D, F, G$ states), $N=4\mathrm{}$ ($S, P, D$ states), and $N=5\mathrm{}$ (${}_{}{}^1{}_{}{}^{}P_{}^{\mathrm{o}}{}_{}{}^{}$ states) ionization thresholds. Two new quantum numbers label the Rydberg series, and are used to predict three "selection rules" for dipole excitation and autoionization processes which agree with experiment. New autoionization widths are reported for the helium states and confirm our group-theoretically predicted selection rules. Our width of 0.151 eV for the ${}_{}{}^1{}_{}{}^{}P_{}^{\mathrm{o}}{}_{}{}^{}$ state at 62.92 eV is in agreement with the recent experimental value 0.132 ± 0.014 eV. Calculations of helium energies and autoionization widths are strongly affected by "avoided crossings" of the doubly excited states as $Z$ is varied continuously. The new quantum numbers project out states in ${\mathrm{H}}^{-}$ which correspond to observed ${}_{}{}^1{}_{}{}^{}P_{}^{\mathrm{o}}{}_{}{}^{}$ shape resonances above the $N=2\mathrm{} \mathrm{and} 3$ ionization thresholds.