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Quantum Electronics

Spontaneous-stimulated annihilation of positronium atoms in the field of intrinsic and external annihilation photons

O. N. Gadomskiĭ, Yu. Yu. Voronov

Published Sep 30, 1996• 0 citations
Publisher

Abstract

The Heisenberg equations of motion for the atomic and photonic operators are used, without recourse to perturbation theory, to calculate the lifetime, energy shift, phase relaxation time and oscillation frequency of a positronium atom under the conditions of two-photon annihilation decay in a field of 'seed' photons.
DOI
10.1070/qe1996v026n09abeh000780

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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 para-positronium atom from two states participating in stimulated optical transitions excited by a laser. It is shown that a non- exponential 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 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.
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, 1 S and 2 P ) 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 1 S state.
The spontaneous radiative decay to the ground state of an atomic system initially in the higher of two excited states, coupled in a radiationless fashion by an external field, is investigated by the method of multiple-time-scale perturbation theory. The coupled differential equations of motion for the probability amplitudes are solved to second order, while the usual secular behavior of conventional time-dependent perturbation theory is eliminated in terms of two natural time scales: a fast time scale corresponding to the reciprocal of the level transition frequency and a slower time scale associated with the inverse of the radiation linewidth. Expressions are obtained to this order for the energy shifts and decay characteristics of the excited states and the energy distribution of the final-state photons, quantities previously determined by Fourier analysis and contour integration and by the phenomenological approach of Weisskopf and Wigner. A detailed comparison of these various methods of solution includes conditions under which the present results agree to second order with the previous calculations.