# Significance of distinct electron correlation effects in determining the P,T-odd electric dipole moment of $^{171}$Yb

## TL;DR

This paper calculates the EDM of $^{171}$Yb considering advanced electron correlation effects using various many-body methods, revealing significant differences from previous estimates due to complex correlation contributions.

## Contribution

It provides the first comprehensive analysis of electron correlation effects on $^{171}$Yb's EDM using all-order relativistic methods, highlighting the importance of non-RPA interactions.

## Key findings

- CCSD results differ significantly from earlier calculations.
- Large correlation effects are due to non-RPA electron interactions.
- Analysis of MBPT(2) and MBPT(3) clarifies the role of different correlation effects.

## Abstract

Parity and time-reversal violating electric dipole moment (EDM) of $^{171}$Yb is calculated accounting for the electron correlation effects over the Dirac-Hartree-Fock (DHF) method in the relativistic Rayleigh-Schr\"odinger many-body perturbation theory, with the second (MBPT(2) method) and third order (MBPT(3) method) approximations, and two variants of all-order relativistic many-body approaches, in the random phase approximation (RPA) and coupled-cluster (CC) method with singles and doubles (CCSD method) framework. We consider electron-nucleus tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions as the predominant sources that induce EDM in a diamagnetic atomic system. Our results from the CCSD method to EDM ($d_a$) of $^{171}$Yb due to the T-PT and NSM interactions are found to be $d_a = 4.85(6) \times 10^{-20} \langle \sigma \rangle C_T \ |e| \ cm$ and $d_a=2.89(4) \times 10^{-17} {S/(|e|\ fm^3)}$, respectively, where $C_T$ is the T-PT coupling constant and $S$ is the NSM. These values differ significantly from the earlier calculations. The reason for the same has been attributed to large correlation effects arising through non-RPA type of interactions among the electrons in this atom that are observed by analyzing the differences in the RPA and CCSD results. This has been further scrutinized from the MBPT(2) and MBPT(3) results and their roles have been demonstrated explicitly.