A model with correction term for the helium atom

Date

2009-09-02T17:22:37Z

Authors

Diacu, Florin N.

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Abstract

We propose a mechanical model for atomic physics. The potential function defining it is formed by the sum of the negative classical Coulomb potential plus a negative homogeneous function of degree -2, which involves the mutual distances between particles, having the role of a correction term. We study the isosceles problem and apply it to the Helium atom. The goal of the paper is to study solutions coming close to collisions. We prove that binary collisions are not possible and restrict our study to triple- and near-triple-collision orbits. We blow-up the triple-collision singularity and paste instead of it, to the phase space, a collision manifold. This is shown to be topologically equivalent to a two-dimensional sphere. The flow on the sphere has two equilibria and is foliated by periodic orbits. We prove the existence of solutions reaching asymptotically these orbits. The set of connecting orbits is finally analysed. We compare the results obtained here with those of a previous paper on Maneff's gravitational law.

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