Structure, branching ratios, and a laser-cooling scheme for the 138BaF molecule

For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable A^'2Δ and A²Π states and, further, the lifetime of the Δ state have been estimated since the loss procedure via the Δ state might fatally break the main quasicycling Σ -Π transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the X²Σ⁺ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and g factors for both X and A states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.