Elaborate wave functions representing low energy positron-helium elastic scattering, which were obtained in the course of calculating accurate values of the scattering phase shifts, are used here to determine the energy distribution of the γ-rays arising from electron-positron annihilation. The results are found to be in excellent agreement with recent experimental measurements. The energy dependence of the electron-positron annihilation rate parameter, Z e f f , is also investigated. It experiences a very sharp rise as the positronium formation threshold is approached, qualitatively in agreement with recent predictions concerning the importance of virtual positronium formation in the annihilation process near the threshold.