Enhanced spin-dependent parity non-conservation effect in the $7s{}^2{S}_{1\mathrm{/}2}\to 6d{}^2{D}_{5\mathrm{/}2}$ transition in Fr: A possibility for unambiguous detection of nuclear anapole moment

Employing the relativistic coupled-cluster method, comparative studies of the parity non-conserving electric dipole amplitudes for the $7s \ ^2S_{1/2} \rightarrow 6d \ ^2D_{5/2}$transitionsin$^{210}$Frand$^{211}$Fr isotopes have been carried out. It is found that these transition amplitudes, sensitive only to the nuclear spin dependent effects, are enhanced by more than 3 orders compared to the low-lying $S-D_{5\mathrm{/}2}$ transitions in Ba${}^{+}$ and Ra${}^{+}$ 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.