Reply to Comment on "Reappraisal of the Electric Dipole Moment Enhancement Factor for Thallium"

TL;DR

This paper defends the authors' recent calculations of thallium's electric dipole moments against critiques, clarifying methodological differences and emphasizing the importance of physical understanding in atomic EDM and PNC computations.

Contribution

It identifies key reasons for discrepancies in EDM calculations, particularly orbital choices and correlation effects, and clarifies the validity of different theoretical approaches.

Findings

Different orbital choices significantly affect EDM results.

Valence-core correlation treatments are crucial for accurate calculations.

The authors' methods produce more reliable EDM estimates for thallium.

Abstract

In a recent Comment [arXiv:1108.3399], Dzuba and Flambaum have referred to the disagreement of the results of our latest calculations of Tl electron and scalar-pseudoscalar (S-PS) electric dipole moments (EDMs) and Cs parity non-conservation (PNC) with some other calculations. We have responded to all their points and also discussed the larger issues related to them. We have attempted to find the reasons for the disagreement between the results of our calculations and those of others. In particular, we have found that the two important reasons for the discrepancies between the Tl EDM calculations of Dzuba and Flambaum and ours are the different choice of single particle orbitals and the treatment of the valence-core correlation effects. We have demonstrated by numerical calculations that the $V^{N-3}$ orbitals used by Dzuba and Flambaum overestimate the Tl electron and S-PS EDMs at the Dirac-Fock level. The failure of their suggested consistency test as interpreted by us is explained for systems with strong correlation like Tl. Also, the importance of understanding the physics underlying different theories on which atomic EDM and PNC calculations are based and comparisons between them are emphasized.