Determination of the scattering lengths of 39K from 1u photoassociation line shapes

We report threshold scattering properties for K-39(f = 1) atoms obtained from analysis of experimental photoassociation spectra of the purely long-range 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 colliding ground state alkali atoms enables us to obtain information on the sign and magnitudes of certain scattering lengths for ground state collisions. Analysis 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, between +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].