Dipole Polarizabilities of the2 S13and2 S01States of He andLi+

Variational calculations of the dipole polarizabilities of the two lowest excited states $2 {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and $2 {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of He and ${\mathrm{Li}}^{+}$ are made with 72-term variational wave functions. Because of the slow convergence for the He $2 {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state, the wave function for this system is extended to include 96 terms. The polarizabilities are determined from the interaction energy of the atomic system with a uniform external electric field. The most complete calculations gave 315.63 atomic units and 801.95 a.u. for He, and 46.88 a.u. and 98.19 a.u. for ${\mathrm{Li}}^{+}$, for the $2 {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and $2 {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ states, respectively. The only previous calculations are those for helium, in which Dalgarno and Kingston used theoretical oscillator strengths. They obtained 313 and 788 a.u. for the $2 {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and $2 {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ states, respectively. The ground states are also calculated as a check on the method used. Excellent agreement with the previous calculations and with experiment is obtained for the ground states of ${\mathrm{H}}^{-}$, He, and ${\mathrm{Li}}^{+}$.