Employing the relativistic coupled-cluster method, comparative studies of the parity nonconserving electric dipole amplitudes for the $7s{}^{2}S_{1/2}\to 6d{}^{2}D_{5/2}$ transitions in ${}^{210}\mathrm{Fr}$ and ${}^{211}\mathrm{Fr}$ 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.

• Received 8 December 2015
• Revised 19 February 2016

DOI:https://doi.org/10.1103/PhysRevA.93.032520