Rotational Splittings in Diatomic Molecules of Interest to Searches for New Physics

Abstract

Diatomic molecules with an energetically low-lying $^3 \Delta_1$ state are attractive platforms to detect new physics beyond the Standard Model, such as parity- and time-reversal violating phenomena. One of the advantages of using a $^3 \Delta_1$ state is its tiny $\Lambda$-splitting due to the coupling between the electronic and rotational angular momenta, which facilitates polarizing the molecules in small external electric fields. Theoretical estimation of the magnitude of the $\Lambda$-splitting is helpful for planning new experiments. In this study, we present a theoretical model to calculate the $\Lambda$-splitting. Our model integrates the relativistic four-component wavefunction and the traditional rotational Hamiltonian based on Hund's case (a). The multireference character of the wavefunction is taken into account. Our calculations for PtH and ThF$^+$ molecules qualitatively agree with experiment. The $\Lambda$-splitting of TaO$^+$ for the rotational ground state is predicted to be around 9 kHz. This tiny splitting can reduce the systematic uncertainty, but in a practical experiment, it may cause depolarization during rotation ramp-up.