A positron beam is produced and accelerated by an electron linear accelerator. The positrons annihilate in-flight when passed through a beryllium foil to produce nearly monoenergetic gamma rays with energies comparable with the positron energy and an energy spread essentially equal to the energy spread of the positron beam, i.e., 2%. Such a 10-MeV gamma-ray beam was collimated and directed at a slab of aluminum that had a thickness corresponding to one mean-free-path for 10-MeV gamma rays. The energy spectra at 0, 15, and 30° to the incident beam were measured with a NaI crystal. The results were integrated and compared with Monte Carlo calculations. The experiments and calculations agreed within the experimental uncertainty.