Leonid V. Skripnikov

The current constraint on the electron electric dipole moment ($e$EDM), $|d_e|<4.1\times 10^{-30}$ ${e {\cdotp} {\rm cm}}$ (90\% confidence), was recently established using the trapped $^{180}$Hf$^{19}$F$^+$ molecular ions in the $J=1$ rotational level of its $ ^3Δ_1$ electronic state [T. S. Roussy, L. Caldwell, T. Wright, et al., arxiv:2212.11841]. The extensive experimental study of the HfF$^+$ cation provides detailed spectroscopy of the $Ω-$doublet levels in the external rotating electric and magnetic fields. We showed that previously developed theoretical approaches can fully reproduce the latest experimental data. Their justification from the first principles is very important for the examination of both modern molecular theory and possible systematic uncertainties in the interpretation of the experimental data obtained with high accuracy.

The AcOH${}^+$ molecular ion is identified as a prospective system to search for $\mathcal{CP}$-violation effects. According to our study AcOH${}^+$ belongs to the class of laser-coolable polyatomic molecular cations implying the large coherence time in the experiments to study symmetry violating effects of fundamental interactions. We perform both nuclear and high level relativistic coupled cluster electronic structure calculations to express experimentally measurable $\mathcal{T}$,$\mathcal{P}$-violating energy shift in terms of fundamental quantities such as the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment ($e$EDM) and dimensionless scalar-pseudoscalar nuclear-electron interaction constant. We further express nuclear MQM in terms of the strength constants of $\mathcal{CP}$-violating nuclear forces: quantum chromodynamics vacuum angle $\barθ$ and quark chromo-EDMs. The equilibrium geometry of AcOH${}^+$ in the ground and the four lowest excited electronic states was found to be linear. The calculated Franck-Condon factors and transition dipole moments indicate that the laser cooling using optical cycle involving the first excited state is possible for the trapped AcOH${}^+$ ions with the Doppler limit estimated to be~$\sim 4$~nK. The lifetime of the (0,1$^1$,0) excited vibrational state considered as a working one for MQM and $e$EDM search experiments is estimated to be $\sim 0.4$ sec.