Photoassociation resonances in the Rb-87(2) 1(g) state dissociating to 5(2)S + 5(2)P(1/2) were produced by the excitation of colliding Rb-87 atoms in a far-off resonance trap. Levels down to 31 cm(-1) below the dissociation limit were measured with resonance linewidths of 15 to 20MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the 5(2)S + 5(2)P(1/2) limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin I = 3 were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters A(nu), vibrational G(nu), and rotational B(nu) parameters. The G(nu) parameters could be fit to an rms accuracy of about 0.01 cm(-1) to a potential constructed from current C-3 and C-6 long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.