Theoretical study of thorium monoxide for the electron electric dipole moment search, II: Electronic properties of $H^3\Delta_1$ in ThO

摘要

Recently an improved limits on the electron electric dipole moment, \eEDM,and dimensionless constant, $k_{T,P}$, characterizing the strength of theT,P-odd pseudoscalar$-$scalar electron$-$nucleus neutral current interaction inthe $H^3\Delta_1$ state of ThO molecule were obtained by ACME collaboration[Science 343, 269 (2014)]. The interpretation of the experiment in terms offundamental quantities \eEDM\ and $k_{T,P}$ is based on the results oftheoretical study of appropriate ThO characteristics, the effective electricfield acting on electron, \Eeff, and a parameter of the T,P-oddpseudoscalar$-$scalar interaction, $W_{T,P}$, given in [J.Chem.Phys.\ 139,221103 (2013)] by St.Petersburg group. To reduce the uncertainties of the givenlimits we report improved calculations of the molecular state$-$specificquantities \Eeff, 81.5~GV/cm, and $W_{T,P}$, 112~kHz, with the uncertaintywithin 7\% of the magnitudes. Thus, the values recommended to use for the upperlimits of the quantities are 75.8~GV/cm and 104~kHz, correspondingly. Thehyperfine structure constant, molecule-frame dipole moment of the $H^3\Delta_1$state and $H^3\Delta_1\to X^1\Sigma^+$ transition energy which, in general, canserve as a measure of reliability of the obtained \Eeff\ and $W_{T,P}$ valuesare also calculated. Besides we report the first calculation of g-factor forthe $H^3\Delta_1$ state of ThO. The results are compared to the earlierexperimental and theoretical studies, and a detailed analysis of uncertaintiesof the calculations is given.