Mountain pass frozen planet orbits in the helium atom model
Dynamical Systems
2024-04-02 v1 Classical Analysis and ODEs
Abstract
We seek frozen planet orbits for the helium atom through an application of the Mountain Pass Lemma to the Lagrangian action functional. Our method applies to a wide class of gravitational-like interaction potentials thus generalising the results in [7] (Cieliebak, Frauenfelder and Volkov - 2023). We also let the charge of the two electrons tend to zero and perform the asymptotic analysis to prove convergence to a limit trajectory having a collision-reflection singularity between the electrons.
Keywords
Cite
@article{arxiv.2404.00307,
title = {Mountain pass frozen planet orbits in the helium atom model},
author = {Stefano Baranzini and Gian Marco Canneori and Susanna Terracini},
journal= {arXiv preprint arXiv:2404.00307},
year = {2024}
}