Precision calculations of the energies of the $\left({2p}^2\right){}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ states of He and ${\mathrm{H}}^{-}$ are carried out with a Hylleraas-type wave function and are the lowest variational results yet obtained. The associated wave functions are used to calculate the mass polarization of the state. With the reduced mass correction, the wave numbers of the transitions $\mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_{}^0{}_{}{}^{}-\left({2p}^2\right){}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ in He and $\mathrm{}\left(2s2p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_{}^0{}_{}{}^{}-\left({2p}^2\right){}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ in ${\mathrm{H}}^{-}$ are found to be 312 222 and 3783 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. This former value is in disagreement with the experiment of Kruger (1930) who obtained 312 118 ${\mathrm{cm}}^{-1\mathrm{}}$. The discrepency between the experimental and theoretical values of 100 ${\mathrm{cm}}^{-1\mathrm{}}$ is large enough to encourage renewed experimental observation.

• Received 13 July 1970

DOI:https://doi.org/10.1103/PhysRevA.2.1667