Relativistic coupled-cluster theory of nuclear spin-dependent parity non-conservation

TL;DR

This paper introduces a relativistic coupled-cluster method to accurately compute nuclear spin-dependent parity non-conservation effects in heavy atoms, enhancing the precision of atomic parity violation calculations.

Contribution

The paper develops a perturbative relativistic coupled-cluster approach with tensor operators for electronic and nuclear spin interactions, enabling precise calculations of parity violating amplitudes.

Findings

Validated method by calculating $E1_{PNC}^{NSD}$ in cesium

Compared results with MBPT diagrams for accuracy

Demonstrated suitability for heavy atom parity violation studies

Abstract

We have developed a relativistic coupled-cluster theory to incorporate nuclear spin-dependent interaction Hamiltonians perturbatively. In this theory, the coupled-cluster operators in the electronic sector are defined as tensor operators of rank one and we introduce suitable diagrammatic representations. For properties calculations, the electronic part is first calculated and later coupled to the nuclear spin part. The method is ideal to calculate parity violating nuclear spin-dependent electric dipole transition amplitudes, $E1_{\rm PNC}^{\rm NSD}$, of heavy atoms. To validate the proposed method the $E1_{\rm PNC}^{\rm NSD}$ of the transition $6\; ^2S_{1/2} \rightarrow 7\; ^2S_{1/2}$ in $^{133}$Cs is calculated for selected MBPT diagrams and compared with the results from our theory.