Employing the relativistic coupled-cluster method, comparative studies of the parity nonconserving electric dipole amplitudes for the 7sS1/22→6dD5/22 transitions in Fr210 and Fr211 isotopes have been carried out. It is found that these transition amplitudes, sensitive only to the nuclear spin-dependent effects, are enhanced substantially owing to the very large contributions from the electron core-polarization effects in Fr. This translates to a relatively large and, in principle, measurable induced light shift, which would be a signature of nuclear spin-dependent parity nonconservation that is dominated by the nuclear anapole moment in a heavy atom like Fr. A plausible scheme to measure this quantity using the Cyclotron and Radioisotope Center (CYRIC) facility at Tohoku University has been outlined.
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