2024/03/30 by Stefano Baranzini, Gian Marco Canneori, Baranzini, Stefano +3
Physics and Astronomy · #Astro and Planetary Science #Astrophysics and Star Formation Studies #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.2404.00307
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.