Abstract
The problem of the interaction of a positronium atom with the field of optical and annihilation photons is considered. The solution obtained for the occupation numbers is used to study kinetics of the annihilation decay of a para-positronium atom from two (for example, 1S and 2P) states participating in stimulated optical transitions excited by a laser. It is shown that a nonexponential time dependence of the occupation numbers is observed under the conditions of a nonlinear coherent interaction of a positronium atom with the field of optical and annihilation photons, and that in some cases there is a possibility of appearance of a long-lived state of a positronium atom with a lifetime hundreds of times longer than the lifetime of a positronium atom in the 1S state.
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