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Electrodynamics of Helium with Retardation and Self-Interaction Effects
Phys. Rev. Lett. 80, 680 – Published 26 January, 1998
DOI: https://doi.org/10.1103/PhysRevLett.80.680
Abstract
We show that an extra constant of motion with an analytic form can exist in the neighborhood of some discrete circular orbits of helium when one includes retardation and self-interaction effects. The energies of these discrete stable circular orbits are in the correct atomic magnitude. The highest frequency in the stable manifold of one such orbit agrees with the highest frequency sharp line of parahelium to within 2%. The generic term of the frequency in the stable manifold to higher orbits is also in agreement with the asymptotic form of quantum mechanics for helium.
References (14)
- M. Poirier, Phys. Rev. A 40, 3498 (1989).
- J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, New York, 1983).
- L. Page, Phys. Rev. 11, 376 (1918).
- J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
- V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
- F. Gustavson, Astron. J. 71, 670 (1966).
- S. Coleman, in Electromagnetism, Paths to Research, D. Teplitz (Plenum, New York, 1982).
- J. De Luca (to be published).
- J. W. Nicholson, Mon. Not. R. Astron. Soc. LXXII, 49 (1912); ibid.LXXII, 139 (1912); ibid.LXXII, 677 (1912); ibid.LXXII, 693 (1912); ibid.LXXII, 729 (1912).
- D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations (Clarendon, Oxford, 1977).
- H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-electron Atoms (Plenum, New York, 1977).
- Ming-Keh Chen, J. Phys. B 27, 4847 (1994).
- N. Bohr, Philos. Mag. 26, 1 (1913); ibid.26, 476 (1913).
- J. De Luca, Braz. J. Phys. 27, 285 (1997).