Stark Effect in Alkali-Metal Ground-State Hyperfine Structure

An atomic-beam magnetic-resonance apparatus with separated oscillatory fields has been used to measure the decrease in the ground-state hyperfine energy separation of ${\mathrm{Cs}}^{133}$, ${\mathrm{Rb}}^{87}$, ${\mathrm{Rb}}^{85}$, ${\mathrm{K}}^{39}$, ${\mathrm{Na}}^{23}$, and ${\mathrm{Li}}^7$ because of the presence of a uniform, static, electric field. The hfs frequency shift due to this quadratic Stark effect is designated by $\delta f=-k\times {10}^{-6\mathrm{}}{E}^2$ Hz/${\mathrm{}(\mathrm{V}/\mathrm{c}\mathrm{m})\mathrm{}}^2$. If the ratio $\frac{\delta f\left(X^A\right)}{\delta f\left({\mathrm{Cs}}^{133}\right)}$ is denoted by ${\kappa }_{X^A}$, then the results are ${\kappa }_{{\mathrm{Rb}}^{87}}=0.546\mathrm{}\left(5\right)\mathrm{}$; ${\kappa }_{{\mathrm{Rb}}^{85}}=0.243\mathrm{}\left(1\right)\mathrm{}$, ${\kappa }_{{\mathrm{K}}^{39}}=0.0315\mathrm{}\left(6\right)\mathrm{}$, ${\kappa }_{{\mathrm{Na}}^{23}}=0.0552\mathrm{}\left(12\right)\mathrm{}$, and ${\kappa }_{{\mathrm{Li}}^7}=0.0270\mathrm{}\left(8\right)\mathrm{}$. Existing theories of the alkali-metal Stark effect are discussed, and none is found to give satisfactory agreement with these experimental ratios.