Potassium ground-state scattering parameters and Born-Oppenheimer potentials from molecular spectroscopy

We present precision measurements with MHz uncertainty of the energy gap between asymptotic and well bound levels in the electronic ground state $X\text{ }{^{1}\ensuremath{\Sigma}}_{\text{g}}^{+}$ of the ${^{39}\text{K}}_{2}$ molecule. The molecules are prepared in a highly collimated particle beam and are interrogated in a $\ensuremath{\Lambda}$-type excitation scheme of optical transitions to long range levels close to the asymptote of the ground state, using the electronically excited state ${A\text{ }^{1}\ensuremath{\Sigma}}_{\text{u}}^{+}$ as the intermediate one. The transition frequencies are measured either by comparison with ${\text{I}}_{2}$ lines or by absolute measurements using a fs-frequency comb. The determined level energies were used together with Feshbach resonances from cold collisions of $^{39}\text{K}$ and $^{40}\text{K}$ reported from other authors to fit ground state potentials. Precise scattering lengths are determined and tests of the validity of the Born-Oppenheimer approximation for the description of cold collisions at this level of precision are performed.