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We have developed a relativistic coupled-cluster theory to incorporatenuclear spin-dependent interaction Hamiltonians perturbatively. This theory isideal to calculate parity violating nuclear spin-dependent electric dipoletransition amplitudes, $E1_{\rm PNC}^{\rm NSD}$, of heavy atoms. Experimentalobservation of which is a clear signature of nuclear anapole moment, thedominant source of nuclear spin-dependent parity violation in atoms and ions.We apply the theory to calculate $E1_{\rm PNC}^{\rm NSD}$ of Cs, which to datehas provided the best atomic parity violation measurements. We also calculate$E1_{\rm PNC}^{\rm NSD}$ of Ba$^+ $ and Ra$^+$, candidates of ongoing andproposed experiments.

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