Periodic orbits and binary collisions in the classical three-body Coulomb problem |
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Authors: | Mitsusada M Sano Kiyotaka Tanikawa |
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Institution: | a Graduate School of Human and Environmental Studies, Kyoto University, Sakyo, Kyoto 606-8501, Japan b National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan |
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Abstract: | In the helium case of the classical three-body Coulomb problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. Focusing our attention on binary collisions with these tools, a sequence of periodic orbits are predicted and are actually found numerically. A family of periodic orbits found has regularity in their actions. For this family of periodic orbits, it is shown that thanks to its regularity, a partial summation of the Gutzwiller trace formula with a daring approximation gives a Rydberg series of energy levels. |
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Keywords: | 05 45 Mt 45 50 Jf 34 10 +x |
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