High-accuracy nuclear-spin-dependent parity-violating amplitudes in Cs133

Relativistic coupled-cluster (RCC) theory at the singles and doubles approximation has been implemented to estimate nuclear-spin-dependent (NSD) parity-violating (PV) electric dipole ($E1$) transition amplitudes (E1PVNSD) among hyperfine levels of the 6s0.28em0ex²S1/2→7s0.28em0ex²S1/2 transition in ¹³³Cs. To validate our calculations, we reproduce the Dirac-Hartree-Fock values and results from the combined coupled-Dirac-Hartree-Fock and random phase approximation (CPDF-RPA) method reported earlier. Contributions from the double-core-polarization (DCP) effects with the CPDF-RPA method were found to be between 3% and 12% among different hyperfine levels. We derived a generalized expression for E1PVNSD, which helped incorporate both the NSD PV Hamiltonian and $E1$ operator simultaneously in the perturbative approach to account for the DCP contributions. The RCC method subsumes the CPDF-RPA and DCP effects in addition to contributions from the Br\"uckner pair correlations and normalization of the wave functions and correlations among them. To improve accuracy of the E1PVNSD amplitudes further, we replace the ab initio values of the $E1$ matrix elements and energies by their experimental values via a sum-over-states approach.