Atomic electric dipole moment induced by the nuclear electric dipole moment: The magnetic moment effect

We have considered a mechanism for inducing a time-reversal violating electric dipole moment (EDM) in atoms through the interaction of a nuclear EDM ${d}_{N}$ with the hyperfine interaction, the ``magnetic moment effect''. We have derived the operator for this interaction and presented analytical formulas for the matrix elements between atomic states. Induced EDMs in the diamagnetic atoms $^{129}\mathrm{Xe}$, $^{171}\mathrm{Yb}$, $^{199}\mathrm{Hg}$, $^{211}\mathrm{Rn}$, and $^{225}\mathrm{Ra}$ have been calculated numerically. From the experimental limits on the atomic EDMs of $^{129}\mathrm{Xe}$ and $^{199}\mathrm{Hg}$ we have placed the following constraints on the nuclear EDMs, $|{d}_{N}({}^{129}\mathrm{Xe})|<1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}|e|\mathrm{cm}$ and $|{d}_{N}({}^{199}\mathrm{Hg})|<2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}|e|\mathrm{cm}$.