Article:
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F. Rupp & J. Scheurle (2010): Genuine Equilibria of Three Body Coulomb
Configurations, Few Body Systems, 48 (1), pp. 1-10.


Abstract:
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The problem analyzed is the classical non-regularized Hamiltonian
formulation of a restricted three body problem under the influence of
Coulomb-interactions. Completing the large literature on Helium-like
systems we will consider the motions around a fixed positive point
charge of (i) one negative and one positive point charge as well as the
“classical” issue of (ii) two negative point charges. Thereby, all our
considerations deal with arbitrary positive and negative charge values
of the mass particles. Here, we give necessary and sufficient conditions
for the existence of genuine equilibria in such systems—recall that
there are none in the usual classical Helium-atom—and analyze their
linearized stability. The thus obtained insights allow us to study the
dynamics near such genuine equilibria.