1S1and2S3States of Helium

The method described previously for the solution of the wave equation of two-electron atoms has been applied to the $1{}_{}{}^1{}_{}{}^{}S$ and $2{}_{}{}^3{}_{}{}^{}S$ states of helium, with the purpose of attaining an accuracy of 0.001 ${\mathrm{cm}}^{-1\mathrm{}}$ in the nonrelativistic energy values. For the $1{}_{}{}^1{}_{}{}^{}S$ state we have extended our previous calculations by solving determinants of orders 252, 444, 715, and 1078, the last yielding an energy value of -2.903724375 atomic units, with an estimated error of the order of 1 in the last figure. Applying the mass-polarization and relativistic corrections derived from the new wave functions, we obtain a value for the ionization energy of 198 312.0258 ${\mathrm{cm}}^{-1\mathrm{}}$, as against the value of 198 312.011 ${\mathrm{cm}}^{-1\mathrm{}}$ derived previously from the solution of a determinant of order 210. With a Lamb shift correction of -1.339, due to Kabir, Salpeter, and Sucher, this leads to a theoretical value for the ionization energy of 198 310.687 ${\mathrm{cm}}^{-1\mathrm{}}$, compared with Herzberg's experimental value of 198 ${310.8}_2$±0.15 ${\mathrm{cm}}^{-1\mathrm{}}$.