A spectroscopic determination of scattering lengths for sodium atom collisions

We report a preliminary value for the zero magnetic field Na S-2(f = 1, m = - 1) + Na S-2(f = 1, m = - 1) scattering length, a(1, - 1). This parameter describes the low-energy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap. Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms. The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum. The observed lineshapes for the purely long-range O-g(-) molecular state enable us to establish key features of the ground state scattering wavefunction. The fortuitous occurrence of a p-wave node near the deepest point (R(e) = 72 a(0)) of the O-g(-) potential curve is instrumental in determining a(1, - 1) = (52 +/- 5) a(0) and a(2,2) = (85 +/- 3) a(0), where the latter is for a collision of two Na S-2(f = 2, m = 2) atoms.