Variational Calculations of the2S3State of Helium

With a 12-parameter Hylleraas-type wave function containing only positive powers, a new calculation has been carried out for the $2{}_{}{}^3{}_{}{}^{}S$ state of helium by the Ritz variational principle. The energy was minimized by a descent process. A nonrelativistic energy of -1.0876088 Hylleraas units was reached as compared with the best previously published value of -1.0876015 Hylleraas units from a 6-parameter function. When masspolarization and ${\alpha }^2{R}_y$ corrections are included, the 12-parameter function gives an ionization potential 2.52 ${\mathrm{cm}}^{-1\mathrm{}}$ less than the experimental value of 38 454.64 ${\mathrm{cm}}^{-1\mathrm{}}$. The electron density at the nucleus is also calculated and compared with the experimental hyperfine-spectrum value. All numerical work was carried out on an I.B.M. 650 computer.