We describe the spectroscopy of highly excited states of ultracold Na-2 mol
ecules using a neu photoassociative approach based on resonantly enhanced m
ultiphoton ionization; We excite a remarkable number of Na-2 rotational sta
tes providing a rich rovibrational spectrum. We thereby extract not only th
e first order quadrupole-quadrupole (C-5) and the van der Waals constants (
C-6) but also sensitive atom-atom interaction parameters such as spin-spin,
spin-orbit, and perturbative constants.