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Theoretical studies of the long lifetimes of the $6d \ ^2D_{3/2,5/2}$ states in Fr: Implications for parity nonconservation measurements

The lifetimes of the $6d \ ^2D_{3/2}$ and $6d \ ^2D_{5/2}$ states in Fr are estimated to be 540(10) ns and 1704(32) ns respectively. They are determined by calculating the radiative transition amplitudes of the allowed electric dipole (E1) and the forbidden electric quadrupole (E2) and magnetic dipole (M1) channels using the second order many-body perturbation theory (MBPT(2)) and the coupled-cluster (CC) method at different levels of approximation in the relativistic framework. These long lifetimes and the large electric dipole parity non conserving amplitudes of $7s \ ^2S_{1/2} \rightarrow 6d \ ^2D_{3/2,5/2}$ transitions strongly favour Fr as a leading candidate for the measurement of parity nonconservation arising from the neutral current weak interaction and the nuclear anapole moment.