The RbSr $^2\Sigma^+$ ground state investigated via spectroscopy of hot & ultracold molecules

We report on spectroscopic studies of hot and ultracold RbSr molecules, and combine the results in an analysis that allows us to fit a potential energy curve (PEC) for the X(1)$^2\Sigma^+$ ground state bridging the short-to-long-range domains. The ultracold RbSr molecules are created in a $\mu$K sample of Rb and Sr atoms and probed by two-colour photoassociation spectroscopy. The data yield the long-range dispersion coefficients $C_6$ and $C_8$, along with the total number of supported bound levels. The hot RbSr molecules are created in a $1000 \,$K gas mixture of Rb and Sr in a heat-pipe oven and probed by thermoluminescence and laser-induced fluorescence spectroscopy. We compare the hot molecule data with spectra we simulated using previously published PECs determined by three different ab-initio theoretical methods. We identify several band heads corresponding to radiative decay from the B(2)$^2\Sigma^+$ state to the deepest bound levels of X(1)$^2\Sigma^+$. We determine a mass-scaled high-precision model for X(1)$^2\Sigma^+$ by fitting all data using a single fit procedure. The corresponding PEC is consistent with all data, thus spanning short-to-long internuclear distances and bridging an energy gap of about 75% of the potential well depth, still uncharted by any experiment. We benchmark ab-initio PECs against our results, and give the PEC fit parameters for both X(1)$^2\Sigma^+$ and B(2)$^2\Sigma^+$ states. As first outcomes of our analysis, we calculate the $s$-wave scattering properties for all stable isotopic combinations and corroborate the locations of Fano-Feshbach resonances between alkali Rb and closed-shell Sr atoms recently observed [Barbe et al., Nat. Phys., 2018, DOI:10.1038/s41567-018-0169-x]. These results should greatly contribute to the generation of ultracold alkali$-$alkaline-earth dimers, whose applications range from quantum simulation to quantum chemistry.