We have measured the intensity dependent rate and frequency shift of a photoassociation transition in a quantum degenerate gas of 7 Li. The rate increases linearly with photoassociation laser intensity for low intensities, whereas saturation is observed at higher intensities. The measured rates and shifts agree reasonably well with theory within the estimated systematic uncertainties. Several theoretically predicted saturation mechanisms are discussed, but a theory in which saturation arises because of quantum mechanical unitarity agrees well with the data. DOI: 10.1103/PhysRevLett.91.080402 PACS numbers: 03.75.Nt, 33.20.Kf, 33.70.-w, 34.20.Cf Photoassociation (PA) of ultracold atoms has been a remarkably useful tool for determining scattering lengths characterizing ultracold atom collisions, for producing ultracold molecules, and for providing extremely precise measurements of atomic radiative lifetimes (see Refs. [1,2] for reviews). This utility is largely a consequence of the spectroscopic precision afforded by the small thermal broadening in a laser or evaporatively cooled gas. Quantum degenerate gases are especially interesting because the coherence of the atomic field may enable the formation of a molecular Bose-Einstein condensate (BEC) from an atomic one by coherent Raman transitions [3,4], stimulated Raman adiabatic passage [5], or by other coherent adiabatic population transfer schemes [6,7].There have been extensive theoretical studies of the rate of PA [8][9][10][11][12]. The rate is predicted to increase linearly with intensity at low intensities, while various mechanisms have been proposed that cause saturation of the rate at higher intensities. Among these mechanisms are the quantum mechanical unitarity limit on the rate of atomic collisions [11], a breakdown of the two-mode approximation [4,13] for PA of Bose condensates caused by coupling to noncondensed atomic modes [12,14 -16], and the depletion of the atomic pair correlation function [15]. Photoassociation resonances are also predicted to exhibit a spectral shift proportional to the light intensity caused by coupling to the continuum of free-atom states [11,[17][18][19]. In contrast to theory, there are relatively few experimental measurements, and only two that could be considered ''precise'' (which we define as measurements with uncertainties of less than a factor of 2). We previously measured the spectral light shift using quantum degenerate 7 Li and obtained good agreement with theory [20]. Both the spectral shift and the PA rate constant were recently measured in a Na condensate, and good agreement with two-body theory was found [21]. Saturation was not observed in this experiment. Saturation was observed in two other lower precision experiments [22,23], but these experiments were performed in a magneto-optical trap, where the temperatures were greater than 100 K and the corresponding unitaritylimited rates were quite small, of the order of 1 s ÿ1 or less.We report precise measurements of both the rate of PA and the spectral shift in...