  Cold quantum gases, when acted upon by electromagnetic fields, can give rise
to samples where isolated atoms coexist with dimers or trimers, which raises
the question of the interactions between these various constituents. Here we
perform microwave photoassociation in a degenerate gas of $^{87}$Rb atoms to
create weakly-bound dimers in their electronic ground state. From the
density-induced shift of the photoassociation line, we measure the atom-dimer
scattering length for the two least-bound states of the molecular potential. We
also determine the complete energy diagram of one hyperfine manifold of the
least-bound state, which we accurately reproduce with a simple model.
