A method and code for calculations of diatomic molecules in the external variable electromagnetic field have been developed. Code applied for calculation of systematics in the electrons electric dipole moment search experiment on ThO $H^3Delta_1$ sta
te related to geometric phases, including dependence on $Omega$-doublet, rotational level, and external static electric field. It is found that systematics decrease cubically with respect to the frequency of the rotating transverse component of the electric field. Calculation confirms that experiment on ThO $H^3Delta_1$ state is very robust against systematic errors related to geometric phases.
We report the results of our theoretical study and analysis of earlier experimental data for the g-factor tensor components of the ground $^2Pi_{1/2}$ state of free PbF radical. The values obtained both within the relativistic coupled-cluster method
combined with the generalized relativistic effective core potential approach and with our fit of the experimental data from [R.J. Mawhorter, B.S. Murphy, A.L. Baum, T.J. Sears, T. Yang, P.M. Rupasinghe, C.P. McRaven, N.E. Shafer-Ray, L.D. Alphei, J.-U. Grabow, Phys. Rev. A 84, 022508 (2011); A. Baum, B.S. thesis, Pomona College, 2011]. The obtained results agree very well with each other but contradict the previous fit performed in the cited works. Our final prediction for g-factors is $G_{parallel}= 0.081(5)$, $G_{perp}=-0.27(1)$.
It is demonstrated that the TaN molecule is the best candidate to search for T,P-violating nuclear magnetic quadrupole moment (MQM), it also looks promising to search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P
-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), scalar$-$pseudoscalar nucleus$-$electron interactions, also of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of $^{181}$Ta MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $theta$ and quark chromo-EDM.
The current limit on the electrons electric dipole moment, $|d_mathrm{e}|<8.7times 10^{-29} e {cdotp} {rm cm}$ (90% confidence), was set using the molecule thorium monoxide (ThO) in the $J=1$ rotational level of its $H ^3Delta_1$ electronic state [Sc
ience $bf 343$, 269 (2014)]. This state in ThO is very robust against systematic errors related to magnetic fields or geometric phases, due in part to its $Omega$-doublet structure. These systematics can be further suppressed by operating the experiment under conditions where the $g$-factor difference between the $Omega$-doublets is minimized. We consider the $g$-factors of the ThO $H^3Delta_1$ state both experimentally and theoretically, including dependence on $Omega$-doublets, rotational level, and external electric field. The calculated and measured values are in good agreement. We find that the $g$-factor difference between $Omega$-doublets is smaller in $J=2$ than in $J=1$, and reaches zero at an experimentally accessible electric field. This means that the $H,J=2$ state should be even more robust against a number of systematic errors compared to $H,J=1$.
