Ground-state scattering lengths for potassium isotopes determined by double-resonance photoassociative spectroscopy of ultracold K

potential. The binding energies of levels within 5 GHz below the lowest ground-state 4s1/2( f a51) 14s1/2( f b51) hyperfine asymptote are measured by both trap loss and ionization detection. The locations of these near-threshold hyperfine-coupled molecular levels allow us to constrain the triplet potential and thereby determine the triplet scattering length. The result for K, at523365a0 (1a050.052 917 7 nm), is a factor of ;5 improvement over previous determinations and establishes that a large K Bose-Einstein condensate will not be stable.