High-accuracy Nuclear Spin Dependent Parity Violating Amplitudes in ${}^{133}$Cs

Abstract

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 ($E{1}_{PV}^{NSD}$) among hyperfine levels of the $6s{}^2{S}_{1/2}\to 7s{}^2{S}_{1/2}$ transition in ${}^{133}$Cs. 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 at the CPDF-RPA method were found to be between 3-12\% among different hyperfine levels. We derived a generalized expression for $E{1}_{PV}^{NSD}$, 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 Brückner pair-correlations and normalization of the wave functions, and correlations among them. To improve accuracy of the $E{1}_{PV}^{NSD}$ amplitudes further, we replace the {\it ab initio} values of the E1 matrix elements and energies by their experimental values via a sum-over-states approach.

arXiv commentv1: 14 pages, 3 Figures, 7 Tables, v2: one Table added, Results and conclusion unchanged

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Cited by in corpus (2)

• Demonstrating Correlation Trends in the Electric Dipole Polarizabilities of Many Low-lying States in Cs I through First-principle Calculations
• Atomic Parity Violation: Standard Model Tests