Relativistic coupled-cluster calculations of nuclear spin-dependent parity non-conservation in Cs, Ba${}^{+}$ and Ra${}^{+}$

We have developed a relativistic coupled-cluster theory to incorporate nuclear spin-dependent interaction Hamiltonians perturbatively. This theory is ideal to calculate parity violating nuclear spin-dependent electric dipole transition amplitudes, $E{1}_{\mathrm{P}\mathrm{N}\mathrm{C}}^{\mathrm{N}\mathrm{S}\mathrm{D}}$, of heavy atoms. Experimental observation of which is a clear signature of nuclear anapole moment, the dominant source of nuclear spin-dependent parity violation in atoms and ions. We apply the theory to calculate $E{1}_{\mathrm{P}\mathrm{N}\mathrm{C}}^{\mathrm{N}\mathrm{S}\mathrm{D}}$ of Cs, which to date has provided the best atomic parity violation measurements. We also calculate $E{1}_{\mathrm{P}\mathrm{N}\mathrm{C}}^{\mathrm{N}\mathrm{S}\mathrm{D}}$ of Ba${}^{+}$ and Ra${}^{+}$, candidates of ongoing and proposed experiments.