Ab initio study of electronic states and radiative properties of the AcF molecule

Relativistic coupled-cluster calculations of the ionization potential, dissociation energy, and excited electronic states under 35,000 cm$^{-1}$ are presented for the actinium monofluoride (AcF) molecule. The ionization potential is calculated to be IP$_e=48,866$ cm$^{-1}$, and the ground state is confirmed to be a closed-shell singlet and thus strongly sensitive to the $\mathcal{T}$,$\mathcal{P}$-violating nuclear Schiff moment of the Ac nucleus. Radiative properties and transition dipole moments from the ground state are identified for several excited states, achieving an uncertainty of $\sim$450 cm$^{-1}$ for the excitation energies. For higher-lying states that are not directly accessible from the ground state, possible two-step excitation pathways are proposed. The calculated branching ratios and Franck-Condon factors are used to investigate the suitability of AcF for direct laser cooling. The lifetime of the metastable $(1)^3\Delta_1$ state, which can be used in experimental searches of the electric dipole moment of the electron, is estimated to be of order 1 ms.