# Analysis of Electric Dipole Moment of $^{225}$Ra Atom using the Relativistic Normal Coupled-cluster Theory

## TL;DR

This paper employs the relativistic normal coupled-cluster theory to accurately calculate the electric dipole moment of $^{225}$Ra, resolving discrepancies from previous methods and providing improved enhancement factors and dipole polarizability values.

## Contribution

The study introduces the use of RNCC theory for EDM calculations, eliminating normalization ambiguities and ensuring natural termination of expressions, leading to more reliable results.

## Key findings

- Enhancement factor for NSM: -6.29(1) x 10^{-17} |e| cm
- Enhancement factor for T-PT e-N: -12.66(14) x 10^{-20} |e| cm
- Dipole polarizability: 244(13) ea_0^3

## Abstract

In view of the large differences in the previous calculations of enhancement factors to the parity and time-reversal violating (P,T-odd) electric dipole moment (EDM) of $^{225}$Ra due to nuclear Schiff moment (NSM) and tensor-pseudotensor (T-PT) electron-nucleus (e-N) interactions between the relativistic coupled-cluster (RCC) theory and other many-body methods, we employ the relativistic normal coupled-cluster (RNCC) theory to explain the discrepancies. The normalization of the wave function in the RNCC theory becomes unity by construction. This feature removes the ambiguity associated with the uncertainties in calculations that could arise due to mismatch in cancellation of the normalization factor of the wave function in a truncated RCC method. Moreover, all the terms in the expression for EDM using the RNCC method naturally terminate, in contrast to the RCC approach. By taking an average of the results from two variants each of both the RCC and RNCC methods, we recommend enhancement factors to the EDM of 225Ra due to NSM as $-$6.29(1) $\times 10^{-17} |e| $cm $( |e| fm^3)$ and due to T-PT e-N coupling constant as $-$12.66(14) $\times {10^{-20} \langle \sigma_N \rangle | e | }$cm, for the nuclear Pauli spinor, $\sigma_N$. This is corroborated by analyzing the dipole polarizability ($\alpha_d$) value of $^{225}$Ra, which is obtained as 244(13) $ea_0^3$. We also compare our results for all three properties with previous calculations that employ different many-body methods. Our $\alpha_d$ value agrees very well with the results that are obtained by carrying out rigorous analyses using other variants of RCC methods.