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Theoretical and Mathematical Physics

One-dimensional model of three-particle resonances

Yu. A. Kuperin, Konstantin A. Makarov, B. S. Pavlov

Published Apr 1, 1985• 10 citations
Publisher
DOI
10.1007/bf01017837

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The solution of many problems in light-induced gas kinetics can be simplified significantly using quantum kinetic equations in the context of the so-called one-dimensional approximation, in which the initial equations are averaged over transverse (relative to the direction of radiation) velocities. The errors introduced in such an approach are usually assumed to be small; however, this has been confirmed quantitatively only on the basis of the simplest (two- and three-level) particle models. We analyze the accuracy of the one-dimensional approximation for multilevel particles quantitatively for the light-induced drift (LID) effect in cesium atoms in the atmosphere of inert buffer gases. It is shown that in the case of the so-called “normal” LID, one-dimensional kinetic equations can always be used instead of three-dimensional equations without a risk of losing some important fine details in the dependence of the drift velocity on the radiation frequency. In the case of anomalous LID, the error of the one-dimensional approximation is also insignificant, but it can be disregarded only in the case of light buffer particles. For comparable masses of resonant and buffer particles, the one-dimensional approximation may give a noticeable error in determination of drift velocity amplitudes; however, the positions of drift velocity zeros and extrema depending on radiation-frequency detuning can be described successfully. Results show that the error introduced by using the one-dimensional approximation for multilevel particles turns out to be more significant than for the simplest particle models.
The decay process of the schematic one-dimensional three-body system is considered. A time-dependent approach is used in combination with a one-dimensional three-body model, which is composed of a heavier core nucleus and two nucleons, with the aim of describing its evolution in two-nucleon emission. The process is calculated from the initial state, in which the three ingredient particles are confined. In this process, two different types of emission can be found: the earlier process includes the emission of spatially correlated two-nucleon pair, like a dinucleon, whereas, at a subsequent time, all the particles are separated from each other. The time-dependent method can be a suitable option to investigate the meta-stable and/or open-quantum systems, where the complicated many-body dynamics should necessarily be taken into account.
In three-level atoms where one level is the ground state and one is a metastable state, even low-intensity resonance radiation can lead to bleaching. This effect causes the radiation trapping to become nonlinear and thus greatly complicates the simulation of such a system. We set up equations to model an optically excited three-level atomic vapor in a two- or three-dimensional cylindrical cell; the model includes the effects of radiation trapping, particle diffusion, and quenching. We then develop a fast and efficient approximate method for the solution of these equations. Results are compared to Monte Carlo simulations; agreement within 15% is achieved.