Coulomb Forces in Three-Particle Atomic and Molecular Systems

  • J. S. Briggs
Part of the Finite Systems and Multiparticle Dynamics book series (FSMD)


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.


Wave Function Quantum Number Helium Atom Born Approximation Nodal Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • J. S. Briggs
    • 1
  1. 1.Fakultät für PhysikAlbert-Ludwigs-UniversitätFreiburgGermany

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