Abstract
In Phys. Rev. D 103, L111303 (2021), we had reported an improved calculation of the nuclear spin-independent parity violating electric dipole transition amplitude ($E1_{PV}$) for the $6s ~ ^2S_{1/2} - 7s ~ ^2S_{1/2}$ transition in $^{133}$Cs by employing a relativistic coupled-cluster (RCC) theory. In a recent Comment, B. M. Roberts and J. S. M. Ginges have raised questions about our calculation of the so-called Core contribution to $E1_{PV}$. Our result for this contribution does not agree with theirs, but is in agreement with results from previous calculations where this contribution is given explicitly. In our reply, we explain in detail the validity of the evaluation of our core contribution. We emphasize that the Main, Core and Tail contributions have been treated on an equal footing in our work unlike the sum-over-states calculations. We also address their concerns about our approximate treatment of the contributions from the QED corrections, which was not the aim of our work, but was carried out for completeness. Nonetheless, conclusion of our above mentioned paper is not going to affect if we replace our estimated QED contribution to $E1_{PV}$ by earlier estimation.
Highlights
In order to set the scene for our reply to the Comment by Roberts and Ginges [1] on our paper [2], we would like to mention that the calculation of the parity violating electric dipole transition amplitude of 133Cs has a long history
There was an unsettled issue about the contributions from the occupied orbitals, referred to as “Core” contribution, to the parity violating electric dipole amplitude (E1PV) of the 6s2S1=2 → 7s2S1=2 transition in the 133Cs atom from the Dirac-Coulomb (DC) Hamiltonian that differed by about 200% between the previous two highprecision calculations reported in Refs. [3,4]
In Ref. [2], we considered the Breit interaction potential and a model quantum electrodynamics (QED) potential along with the DC Hamiltonian to include its contributions to all-orders in the residual interaction using the relativistic coupled-cluster (RCC) theory
Summary
In order to set the scene for our reply to the Comment by Roberts and Ginges [1] on our paper [2], we would like to mention that the calculation of the parity violating electric dipole transition amplitude of 133Cs has a long history. The corrections due to the exchange of transverse photons between pairs of electrons, known as the Breit interaction, and the quantum electrodynamics (QED) interactions were included to improve the atomic wave function in the RCCSDT method This method was evaluated to use the Main, Core and Tail contributions on an equal footing. The reasons for the disagreement for the Core contribution for Cs between the results referred to by Roberts and Ginges and ours is the difference in the physical effects included in the two works and the improper scaling of the atomic wave functions to compensate for the missing physical effects in the evaluation of E1PV. Contributions to E1PV arise mainly from the S state of a S ↔ D3=2 transition in Raþ
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