Two-photon Doppler-free spectroscopy has been used to measure Stark shifts of $n{}_{}{}^2{}_{}{}^{}S$ Rydberg states of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ (for $n=15\mathrm{} \mathrm{to} 80$). Scalar polarizabilities ${\alpha }_0$ were found to obey the relation ${\alpha }_0[\mathrm{in}\mathrm{MHz}/{(\mathrm{V}/\mathrm{cm})}^2]=2.202\mathrm{}\left(28\right)\mathrm{}\times {10}^{-9\mathrm{}}{n}^{*6\mathrm{}}+5.53\mathrm{}\left(13\right)\mathrm{}\times {10}^{-11\mathrm{}}{n}^{*7\mathrm{}}$, in good agreement with theoretical values. Avoided crossings were also determined, and first avoided crossings (with the $n-3\mathrm{}$ manifold of levels) fitted the relation $E(\mathrm{in}\mathrm{V}/\mathrm{cm})=4.638\mathrm{}\left(6\right)\mathrm{}\times \frac{{10}^8}{n^{*5\mathrm{}}}+1.528\mathrm{}\left(18\right)\mathrm{}\times \frac{{10}^{10}}{n^{*7\mathrm{}}}$.

• Received 10 August 1984

DOI:https://doi.org/10.1103/PhysRevA.31.2718