Determination of the scattering lengths of K-39 from 1(u) photoassociationline shapes

We report threshold scattering properties for K-39(f = 1) atoms obtained fr om analysis of experimental photoassociation spectra of the purely long-ran ge K-39(2) lit state. The existence of hyperfine structure in the excited K -2, 1(u) state and a knowledge of the Hamiltonian structure for two collidi ng ground state alkali atoms enables us to obtain information on the sign a nd magnitudes of certain scattering lengths for ground state collisions. An alysis of the experimental photoassociation line shapes shows that the 39K scattering lengths are between -3.2 and +0.8 nm (-60a(0) and +15a(0), where 1a(0) = 1 a.u. = 0.0529177 nm) for the a (3)Sigma(u)(+) molecular state, b etween +4.8 and +12 nm (+90a(0) and +230a(0)) for the X(1)Sigma(g)(+) state , and between -7.9 and +1.1 nm (-150a(0) and +20a(0)) for collisions of two f = 1, m = -1 atoms. [S1050-2947(99)03612-4].