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# Combined 4-component and relativistic pseudopotential study of ThO for the electron electric dipole moment search

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### Abstract

A precise theoretical study of the electronic structure of heavy atom diatomic molecules is of key importance to interpret the experiments in the search for violation of time-reversal (T) and spatial-parity (P) symmetries of fundamental interactions it terms of the electron electric dipole moment, eEDM, and dimensionless constant, $$k_{T,P}$$, characterizing the strength of the T,P-odd pseudoscalar$$-$$scalar electron$$-$$nucleus neutral current interaction. ACME collaboration has recently obtained and improved limits on these quantities using a beam of ThO molecules in the $$H^3\Delta_1$$ state [Science 343, 269 (2014)]. We apply the combined direct 4-component and two-step relativistic pseudopotential/restoration approaches to a benchmark calculation of the effective electric field, Eeff, parameter of the T,P-odd pseudoscalar$$-$$scalar interaction, $$W_{T,P}$$, and HFS constant in $$^3\Delta_1$$ state of the ThO molecule. The first two parameters are required to interpret the experimental data in terms of the eEDM and $$k_{T,P}$$ constant. We have investigated the electron correlation for all of the 98 electrons of ThO simultaneously up to the level of the coupled cluster with single, double and noniterative triple amplitudes theory. Contributions from iterative triple and noniterative quadruple cluster amplitudes for the valence electrons have been also treated. The obtained values are Eeff=79.9 GV/cm, $$W_{T,P}$$=113.1 kHz. The theoretical uncertainty of these values we estimate as about two times smaller than that of our previous study [JCP, 142, 024301 (2015)]. It was found that the correlation of the inner- and outer- core electrons contributes 9% to the effective electric field. The values of the molecule frame dipole moment of the $$^3\Delta_1$$ state and the $$H^3\Delta_1\to X^1\Sigma^+$$ transition energy of ThO calculated within the same methods are in a very good agreement with the experiment.

### Most cited references2

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### An electron electric dipole moment search in theX3Δ1ground state of tungsten carbide molecules

(2009)
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### Application of a Relativistic Coupled-Cluster Theory to the Effective Electric Field in YbF

(2014)
An accurate determination of the effective electric field (Eeff) in YbF is important, as it can be combined with the results of future experiments to give an improved new limit for the electric dipole moment of the electron. We report a relativistic coupled-cluster calculation of this quantity in which all the core electrons were excited. It surpasses the approximations made in the previous reported calculations. We obtain a value of 23.1 GV/cm for Eeff in YbF with an estimated error of less than 10%. The crucial roles of the basis sets and the core excitations in our work are discussed.
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### Author and article information

###### Journal
2016-10-04
###### Article
1610.00994