Model three-body problem in the molecular mass limit |
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Authors: | AC Fonseca PE Shanley |
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Institution: | Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742 USA;Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556 USA |
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Abstract: | The bound states of a three-body molecule composed of two identical heavy nuclei and a light “electron” interacting through short-range s-wave potentials are studied. The spectrum of three-body bound states grows as the mass ratio m between the heavy and light particles increases, and presents a remarkable vibration rotation structure that can be fitted with the usual empirical energy formulas of molecular spectroscopy. The results of the exact three-body calculation for the binding energy and bound-state wavefunction are compared with the predictions of the Born-Oppenheimer method for the same system. We find that for m > 30, the Born-Oppenheimer approximation yields very good results for both the binding energies and wavefunctions. For smaller m (1 <m < 30) the Born-Oppenheimer results are still surprisingly good and this is shown to be related to the range of the two-body interactions. |
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