Mountain pass frozen planet orbits in the helium atom model

  • Stefano Baranzini

    Università degli Studi di Torino, Torino, Italy
  • Gian Marco Canneori

    Università degli Studi di Torino, Torino, Italy
  • Susanna Terracini

    Università degli Studi di Torino, Torino, Italy
Mountain pass frozen planet orbits in the helium atom model cover

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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 Cieliebak, Frauenfelder, and Volkov [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), 379–455]. We also let the charges of the two electrons tend to zero and perform an asymptotic analysis to prove convergence to a limit trajectory having a collision-reflection singularity between the electrons.

Cite this article

Stefano Baranzini, Gian Marco Canneori, Susanna Terracini, Mountain pass frozen planet orbits in the helium atom model. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2024), published online first

DOI 10.4171/AIHPC/140