Variational Calculations of Energy and Fine Structure for the2P3State of Helium

Using an 18-parameter Hylleraas-type wave function containing only positive powers, a calculation has been carried out for the $2{}_{}{}^3{}_{}{}^{}P$ state of helium by the Ritz variational principle. Breit's reduction was used to convert the problem from six to three variables. The energy was minimized by the approximate solution of an eigenvalue problem. With this wave function the fine structure splitting was calculated. Our best wave function yields an energy 15.5 ${\mathrm{cm}}^{-1\mathrm{}}$ above the experimental value while the corresponding fine structure splitting is in error by about 1 part in ${10}^2$. All computation was carried out on an IBM-650 computer.