Variational calculations for excited states in He i: Improved estimation of the ionization energy from accurate energies for the n3S, n1D, n3D series

Variational calculations with correlated basis sets have been carried out to obtain the nonrelativistic energies for the n ${}^3$S (n=2–6), n ${}^1$D (n=3–8), and n ${}^3$D (n=3–8) series in He i with estimated accuracies of ${10}^{\mathrm{-}3}$–${10}^{\mathrm{-}5}$ ${\mathrm{cm}}^{\mathrm{-}1}$. A comparison of the results with recently reevaluated experimental energy values, with the aid of available relativistic and mass-polarization corrections, suggests a value of 198 310.773(1) ${\mathrm{cm}}^{\mathrm{-}1}$ for the ionization energy for He i on an energy scale fixed by the 2 ${}^1$P value of 171 135.0000 ${\mathrm{cm}}^{\mathrm{-}1}$.