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Title: Classical helium atom with radiation reaction

Abstract

We study a classical model of helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori conceivable solutions of the problem, those corresponding to the emission of an infinite amount of energy. We show that the Dirac prescription solves a problem of inconsistency plaguing all available models which neglect radiation reaction, namely, the fact that in all such models, most initial data lead to a spontaneous breakdown of the atom. A further modification is that the system thus acquires a peculiar form of dissipation. In particular, this makes attractive an invariant manifold of special physical interest, the zero-dipole manifold that corresponds to motions in which no energy is radiated away (in the dipole approximation). We finally study numerically the invariant measure naturally induced by the time-evolution on such a manifold, and this corresponds to studying the formation process of the atom. Indications are given that such a measure may be singular withmore » respect to that of Lebesgue.« less

Authors:
 [1]; ;  [2]
  1. Universita degli Studi di Milano, Corso di Laurea in Fisica, Via Celoria 16, I-20133 Milano (Italy)
  2. Dipartimento di Matematica, Universita degli Studi di Milano, Via Saldini 50, I-20133 Milano (Italy)
Publication Date:
OSTI Identifier:
22093606
Resource Type:
Journal Article
Journal Name:
Chaos (Woodbury, N. Y.)
Additional Journal Information:
Journal Volume: 22; Journal Issue: 2; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; ATOMS; AUTOIONIZATION; BREAKDOWN; DIPOLES; ELECTRODYNAMICS; EMISSION; EVOLUTION; HELIUM; MATHEMATICAL SOLUTIONS; MODIFICATIONS

Citation Formats

Camelio, G., Carati, A., and Galgani, L. Classical helium atom with radiation reaction. United States: N. p., 2012. Web. doi:10.1063/1.4703945.
Camelio, G., Carati, A., & Galgani, L. Classical helium atom with radiation reaction. United States. doi:10.1063/1.4703945.
Camelio, G., Carati, A., and Galgani, L. Fri . "Classical helium atom with radiation reaction". United States. doi:10.1063/1.4703945.
@article{osti_22093606,
title = {Classical helium atom with radiation reaction},
author = {Camelio, G. and Carati, A. and Galgani, L.},
abstractNote = {We study a classical model of helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as pointed out by Dirac, in any model of classical electrodynamics of point particles involving radiation reaction one has to eliminate, from the a priori conceivable solutions of the problem, those corresponding to the emission of an infinite amount of energy. We show that the Dirac prescription solves a problem of inconsistency plaguing all available models which neglect radiation reaction, namely, the fact that in all such models, most initial data lead to a spontaneous breakdown of the atom. A further modification is that the system thus acquires a peculiar form of dissipation. In particular, this makes attractive an invariant manifold of special physical interest, the zero-dipole manifold that corresponds to motions in which no energy is radiated away (in the dipole approximation). We finally study numerically the invariant measure naturally induced by the time-evolution on such a manifold, and this corresponds to studying the formation process of the atom. Indications are given that such a measure may be singular with respect to that of Lebesgue.},
doi = {10.1063/1.4703945},
journal = {Chaos (Woodbury, N. Y.)},
issn = {1054-1500},
number = 2,
volume = 22,
place = {United States},
year = {2012},
month = {6}
}