Perturbation theory for the Stark effect in the hyperfine structure of alkali-metal atoms

We have studied the quadratic Stark effect on the hyperfine structure in the ground states of the alkali-metal atoms, lithium through cesium. In evaluating the leading perturbation terms, we have utilized two sets of first-order wave functions, corresponding respectively to perturbations of the atomic wave functions by the electric field and by the nuclear moment. The perturbed wave-functions were obtained by solving the appropriate differential equations in first-order perturbation theory. The theoretical results agree very well with the recent experimental data for the entire series of alkali-metal atoms. A discussion of the relation of our theoretical results to earlier ones in some of the alkali-metal atoms is also presented.