Reexamination of the ground state Born-Oppenheimer Yb$_2$ potential

Abstract: The precision of the photoassociation spectroscopy of Yb dimer in degenerate gases is enough to improve the constraints on the new short-range gravity-like forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [M. Borkowski et al. Sci. Rep. A {\bf 9}, 14807 (2019)]. The ground-state interaction potential of ytterbium dimer is investigated at the eXact 2-component core-correlated CCSD(T) level of {\it ab initio} theory in the complete basis set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. Empirical constraint on the number of bound vibrational energy levels of the $^{174}$Yb$_2$ dimer is accounted for by representing the global {\it ab initio}-based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on the short-range gravity-like forces by ultracold atomic spectroscopy.