Measurement and modeling of hyperfine- and rotation-induced state mixing in large weakly bound sodium dimers

We present high-precision trap loss spectroscopy of excited Na{sub 2} molecules obtained by the photoassociation of ultracold sodium atoms. Near the 3 {sup 2}S+3 {sup 2}P{sub 3/2} dissociation limit, hyperfine and rotational (Coriolis-type) interactions cause significant mixing of states of different nominal Hund's case (c) symmetry resulting in a complex pattern of spectral lines. We construct a theoretical model of the large, slowly rotating molecule starting from a long-range, atomic viewpoint. Interaction potentials are derived from the known long-range resonant dipole and van der Waals forces between atoms, supplemented at short range by the results of ab initio electronic-structure calculations. Spin-dependent interactions coupling the various angular momenta--nuclear spin, electron spin, electron orbit, and the mechanical rotation of the molecule as a whole--are derived from known atomic parameters. We avoid imposing approximate symmetries or coupling schemes and consequently include all nonadiabatic mixing of different degrees of freedom. Quantitative agreement between experiment and theory for both line positions and intensities is found. Specifically, we observe and calculate mixing of levels of 0{sub g}{sup -}, 0{sub u}{sup +}, and 1{sub g} symmetry bound by