The diatomic Hartree model at dissociation

We study the Hartree model for two electrons with spin, living in the two-dimensional or three-dimensional space with Coulomb interactions and submitted to the potential induced by two nuclei of charge +1. In the limit where the nuclei move away from each other, we show that the two lowest eigenfunctions of the mean-field Hamiltonian are asymptotically given by an even, respectively odd, superposition of the minimiser associated with the corresponding Hartree one nucleus model. We then give upper and lower bounds on the exponentially small gap between the first two eigenvalues, due to (nonlinear) quantum tunneling.

Automated summary

This study focuses on the Hartree model for two electrons with spin in two-dimensional or three-dimensional space, considering Coulomb interactions and the potential induced by two nuclei with charge +1. The research demonstrates the behavior of the two lowest eigenfunctions of the mean-field Hamiltonian as the nuclei move apart, and provides bounds on the gap between the first two eigenvalues due to quantum tunneling effects.