Ground-state properties of Ca${}_2$ from narrow line two-color photoassociation

By two-color photoassociation of ${}^{40}$Ca four weakly bound vibrational levels in the Ca${}_2$ \Xpot ground state potential were measured, using highly spin-forbidden transitions to intermediate states of the coupled system ${}^3{\mathrm{\Pi }}_u$ and ${}^3{\mathrm{\Sigma }}_u^{+}$ near the ${}^3{P}_1$+${}^1{S}_0$ asymptote. From the observed binding energies, including the least bound state, the long range dispersion coefficients ${\mathrm{C}}_6,{\mathrm{C}}_8,{\mathrm{C}}_{10}$ and a precise value for the s-wave scattering length of 308.5(50)~$a_0$ were derived. From mass scaling we also calculated the corresponding scattering length for other natural isotopes. From the Autler-Townes splitting of the spectra, the molecular Rabi frequency has been determined as function of the laser intensity for one bound-bound transition. The observed value for the Rabi-frequency is in good agreement with calculated transition moments based on the derived potentials, assuming a dipole moment being independent of internuclear separation for the atomic pair model.