We report the first observation of electron momentum contributions to the D
oppler broadening of radiation produced by in-flight two-photon annihilatio
n in solids. In these experiments an approximately 2.5 MeV positron beam im
pinged on thin polyethylene, aluminum, and gold targets. Since energetic po
sitrons easily penetrate the nuclear Coulomb potential and do not cause a s
trong charge polarization. the experimental annihilation line shapes agree
well with calculations based on a simple independent particle model. Moreov
er, annihilations with the deepest cure electrons are greatly enhanced.