[en] The cooling and trapping of atoms and atomic ions is a rapidly advancing field of fundamental science (e.g., Bose-Einstein condensation). We are attempting to extend the field to neutral molecules as well. As a first step, we are studying single- and multicolor photoassociation of ultracold (∼300 μK) ³⁹K atoms confined in a magneto-optical trap. Photoassociation of ultracold atoms (as opposed to thermal atoms) includes sharp resonances with wavelength as long-range rovibrational levels (outer turning points of tens or hundreds of Bohr) are accessed from colliding atomic pairs with ∼10 MHz of relative kinetic energy and only a few partial waves (l=0,1,2). Potential energy curves derived from these spectra test electronic structure and long-range perturbation theory calculations of interatomic potentials. In particular, such studies yield the full set of potential energy curves needed for fully quantum calculations of atomic line broadening at any temperature