Determination of39Kscattering lengths using photoassociation spectroscopy of the0g−state

Threshold scattering properties of ${}^{39}\mathrm{K}$ atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\prime }=0\mathrm{}–6)$ populated in the photoassociation process $\mathrm{K}\mathrm{}\left(4S\right)+\mathrm{K}\mathrm{}\left(4S\right)+ħ\overrightarrow{\omega }{\mathrm{K}}_2^{*}\left[0_g^{-}{(v}^{\prime }{,J}^{\prime }\right)].$ The measured spectra exhibit several general trends, including large $J^{\prime }=2\mathrm{}$ linewidths, large relative $J^{\prime }=4\mathrm{}$ peak intensities, and odd rotational lines which are weak or missing. The even $J^{\prime }$ 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, $a_s{=140\mathrm{}}_{-9}^{+6\mathrm{}}$ a.u. and $a_t=-17-{0.045(C}_6-C_6)\pm 25$ a.u., $C_6=3800\mathrm{}$ a.u.