On the Feasibility of Rovibrational Laser Cooling of Radioactive RaF$^{+}$ and RaH$^{+}$ Cations

Polar radioactive molecules have been suggested to be exceptionally sensitive systems in the search for signatures of symmetry-violating effects in their structure. Radium monofluoride (RaF) possesses an especially attractive electronic structure for such searches, as the diagonality of its Franck-Condon matrix enables the implementation of direct laser cooling for precision experiments. To maximize the sensitivity of experiments with short-lived RaF isotopologues, the molecular beam needs to be cooled to the rovibrational ground state. Due to the high kinetic energies and internal temperature of extracted beams at radioactive ion beam (RIB) facilities, in-flight rovibrational cooling would be restricted by a limited interaction timescale. Instead, cooling techniques implemented on ions trapped within a radiofrequency quadrupole cooler-buncher can be highly efficient due to the much longer interaction times (up to seconds). In this work, the feasibility of rovibrationally cooling trapped RaF$^{+}$ and RaH$^{+}$ cations with repeated laser excitation is investigated. Due to the highly diagonal nature between the ionic ground state and states in the neutral system, any reduction of the internal temperature of the molecular ions would largely persist through charge-exchange without requiring the use of cryogenic buffer gas cooling. Quasirelativistic X2C and scalar-relativistic ECP calculations were performed to calculate the transition energies to excited electronic states and to study the nature of chemical bonding for both RaF$^{+}$ and RaH$^{+}$. The results indicate that optical manipulation of the rovibrational distribution of trapped RaF$^{+}$ and RaH$^{+}$ is unfeasible due to the high electronic transition energies, which lie beyond the capabilities of modern laser technology. However, more detailed calculations of the structure of RaH+ might reveal possible laser-cooling pathways.