Determination of ³⁹K scattering lengths using photoassociation spectroscopy of the 0_g^- state

Threshold scattering properties of ³⁹K atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels (v^′=0–6) populated in the photoassociation process K(4S)+K(4S)+ħω⃗K₂^*[0_g^-(v^′,J^′)]. The measured spectra exhibit several general trends, including large J^′=2 linewidths, large relative J^′=4 peak intensities, and odd rotational lines which are weak or missing. The even J^′ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, a_s=140_-9⁺⁶ a.u. and a_t=-17-0.045(C₆-C₆)±25 a.u., C₆=3800 a.u.