Hyperfine-mediated static polarizabilities of monovalent atoms and ions

We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowledge of this transition polarizability is required in a number of high-precision experiments, such as microwave atomic clocks and searches for $\mathit{CP}$-violating permanent electric dipole moments. While the traditional polarizability arises in the second order of interaction with the externally applied electric field, the differential polarizability involves an additional contribution from the hyperfine interaction of atomic electrons with nuclear moments. We derive formulas for the scalar and tensor polarizabilities including contributions from magnetic dipole and electric quadrupole hyperfine interactions. Numerical results are presented for Al, Rb, Cs, ${\mathrm{Yb}}^{+}$, ${\mathrm{Hg}}^{+}$, and Fr.

Figure 1

Diagrams representing the complete third-order hyperfine-mediated polarizability. Each diagram contains a hyperfine interaction (horizontal line capped with a filled square) in addition to two interactions with the external electric field (horizontal line capped with an empty triangle). The diagrams correspond to the (a) top, (b) center, (c) bottom, and (d) normalization terms discussed in the text.