Stark effect of the cesium ground state: electric tensor polarizability and shift of the clock transition frequency

We present a theoretical analysis of the Stark effect in the hyperfine structure of the cesium ground-state. We have used third order perturbation theory, including diagonal and off-diagonal hyperfine interactions, and have identified terms which were not considered in earlier treatments. A numerical evaluation using perturbing levels up to n=18 yields new values for the tensor polarizability $\alpha_2(6S_{1/2})$ and for the Stark shift of the clock transition frequency in cesium. The polarizabilities are in good agreement with experimental values, thereby removing a 40-year-old discrepancy. The clock shift value is in excellent agreement with a recent measurement, but in contradiction with the commonly accepted value used to correct the black-body shift of primary frequency standards.