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Coulomb Forces in Three-Particle Atomic and Molecular Systems

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Coulomb Interactions in Nuclear and Atomic Few-Body Collisions

Part of the book series: Finite Systems and Multiparticle Dynamics ((FSMD))

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Abstract

In the solution of atomic and molecular few-body problems one is in the fortunate position that the force operating, the Coulomb force, is known exactly and has a simple analytic form both in configuration and momentum space. For systems involving nuclei of low charge the situation is even simpler since relativistic and quantum-electrodynamic effects can also be neglected in most cases. Then it appears remarkable that even the simplest few-body Coulomb problem, that involving three particles, is still not solved completely. The reason is equally simple. The infinite range of the Coulomb force and the singular behavior at the origin, both in configuration and momentum space, result in mathematical difficulties not present for short-range potentials. For example, traditional formal scattering theory is not applicable and must be modified appropriately. Similarly in the formation of resonances in two-electron atoms and in the motion in states of the three-body continuum, the correlation between the particles extends to infinite separation; the motion is never free. Of course this feature is well understood in the two-body Coulomb problem, which luckily is soluble in closed form in both the quantum-mechanical and classical cases. The infinite-range force results in an infinite number of bound states converging to the two-body breakup threshold.

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Authors and Affiliations

  1. Fakultät für Physik, Albert-Ludwigs-Universität, D-79104, Freiburg, Germany

    J. S. Briggs

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  1. J. S. Briggs
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Editor information

Editors and Affiliations

  1. Brown University, Providence, Rhode Island, USA

    Frank S. Levin

  2. University of Florida, Gainesville, Florida, USA

    David A. Micha

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© 1996 Springer Science+Business Media New York

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Briggs, J.S. (1996). Coulomb Forces in Three-Particle Atomic and Molecular Systems. In: Levin, F.S., Micha, D.A. (eds) Coulomb Interactions in Nuclear and Atomic Few-Body Collisions. Finite Systems and Multiparticle Dynamics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9880-7_5

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  • DOI: https://doi.org/10.1007/978-1-4757-9880-7_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9882-1

  • Online ISBN: 978-1-4757-9880-7

  • eBook Packages: Springer Book Archive

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