Scalar-pseudoscalar interaction in the francium atom

Fr atom can be successively used to search for the atomic permanent electric dipole moment (EDM) [Hyperfine Interact. 236, 53 (2015); J. Phys.: Conference Series 691, 012017 (2016)]. It can be induced by the permanent electron EDM predicted by modern extensions of the standard model to be nonzero at the level accessible by the new generation of EDM experiments. We consider another mechanism of the atomic EDM generation in Fr. This is caused by the scalar-pseudoscalar nucleus-electron neutral current interaction with the dimensionless strength constant $k_{T,P}$. Similar to the electron EDM this interaction violates both spatial parity and time-reversal symmetries and can also induce permanent atomic EDM. It was shown in [Phys. Rev. D 89, 056006 (2014)] that the scalar-pseudoscalar contribution to the atomic EDM can dominate over the direct contribution from the electron EDM within the standard model. We report high-accuracy combined all-electron and two-step relativistic coupled cluster treatment of the effect from the scalar-pseudoscalar interaction in the Fr atom. Up to the quadruple cluster amplitudes within the coupled cluster method with single, double, triple, and noniterative quadruple amplitudes, CCSDT(Q), were included in correlation treatment. This calculation is required for the interpretation of the experimental data in terms of $k_{T,P}$. The resulted EDM of the Fr atom expressed in terms of $k_{T,P}$ is $d_{\mathrm{Fr}}=k_{T,P}4.50\times {10}^{-18}e\mathrm{cm}$, where $e$ is the (negative) charge of the electron. The value of the ionization potential of the ${}^2{S}_{1/2}$ ground state of Fr calculated within the same methods is in very good agreement with the experimental datum.

Figure 1

The dependence of the contribution to $R_s$ from the spin polarization of the space-polarized $1s$—$3d$ orbitals of Fr on ${\epsilon }_{\mathrm{virt},\max }^{\left(0\right)}$, in percentage of the total PT2 contribution from the electrons. ${\epsilon }_{\mathrm{virt},\max }^{\left(0\right)}$ is the energy of the highest considered virtual orbital in Eq. (8). 100% corresponds to ${\epsilon }_{\mathrm{virt},\max }^{\left(0\right)}=6500$ a.u.