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Short range interactions in a two-electron system: energy levels and magnetic properties

The problem of two electrons in a square billiard interacting via a finite-range repulsive
Yukawa potential and subjected to a constant magnetic field is considered. We compute
the energy spectrum for both singlet and triplet states, and for all symmetry classes, as a
function of the strength and range of the interaction and of the magnetic field. We show
that the short-range nature of the potential suppresses the formation of “Wigner
molecule” states for the ground state, even in the strong interaction limit. The magnetic
susceptibility \chi(B) shows low-temperature paramagnetic peaks due to exchange
induced singlet-triplet oscillations. The position, number and intensity of these peaks depend
on the range and strength of the interaction. The contribution of the interaction to the
susceptibility displays paramagnetic and diamagnetic phases as a function of T.

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