Induced decay of positronium and grasers

The differential cross section and the total cross section for the stimulated decay of positronium by an incident photon of frequencyΩ is calculated as a function of the dimensionless variableξ=hΩ/mc ². Forξ?1 the total cross section is found to decrease asξ ^?2. We also look at the particular case of positronium in a black-body radiation field. Expressions for the number of induced annihilations per second as functions of the dimensionless ratiomc ²/kT and the number of positronium atoms are obtained. It is found that this rate is proportional to (kT/mc ²)² forkT?mc ² and to (kT/mc ²)ln(kT/mc ²) forkT?mc ². The possibility of utilizing induced two-photon decay of positronium as a γ-ray laser at the wavelength λ _C /2 is examined, where λ _C is the Compton wavelength.