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We study the Hartree model for two electrons with spin, living in thetwo-dimensional or three-dimensional space with Coulomb interactions andsubmitted to the potential induced by two nuclei of charge +1. In the limitwhere the nuclei move away from each other, we show that the two lowesteigenfunctions of the mean-field hamiltonian are asymptotically given by aneven, respectively odd, superposition of the minimizer associated with thecorresponding Hartree one nucleus model. We then give upper and lower bounds onthe exponentially small gap between the first two eigenvalues, due to(nonlinear) quantum tunneling.

The diatomic Hartree model at dissociation