We have studied the energetic proton and alpha particle populations during the extended downstream region of three quasi-parallel interplanetary shock events. The observations were carried out using the University of Maryland/Max-Planck-Institut ISEE 3 ULECA (Ultra Low Energy Charge Analyzer) sensor, which unambiguously identifies protons and alphas using the electrostatic deflection versus residual energy technique. The downstream particles exhibit anisotropies due largely, but not entirely, to convection in the solar wind. Using a detailed technique to find the reference frame in which the particle distribution functions are isotropic, we find that this frame is moving with respect to the solar wind at speeds from tens to hundreds of kilometers/second, is usually within ~20% of the magnetic field direction, and is directed toward the Sun. We identify this reference frame as the rest frame of the scattering centers which isotropize the particle distribution functions. In the solar frame the scattering center frame sometimes moves at the Alfv¿n velocity, but just as often it has significantly higher or lower velocity. The spectral indices of the proton and alpha distribution functions are found to be remarkably constant during the downstream period, being generally insensitive to changes in particle flux levels, magnetic field direction, and solar wind densities. In two of the three events the proton and alpha spectra are the same throughout the entire downstream period, in agreement with predictions of diffusive shock acceleration theory. We find that diffusive acceleration theory cannot predict the particle spectra using only solar wind data. However, using the scattering center velocities, we are able to correctly predict the particle spectra indices for these three events. ¿ American Geophysical Union 1988