Abstract
A Monte Carlo method is described for simulating the trajectories and annihilation of positrons in matter. The technique is applied to the calculation of annihilation spectra of slow positrons in helium gas at several temperatures and with various assumed distributions for the initial positron momenta. The results obtained are essentially independent of the initial momentum distribution and are in excellent agreement with the available experimental and theoretical data. Advantages of the Monte Carlo formulation for treating a wide range of problems in positron annihilation are discussed.