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Michelangeli, Alessandro and Pfeiffer, Paul (2016): Stability of the (2+2)-fermionic system with zero-range interaction. In: Journal of Physics A-Mathematical and theoretical, Vol. 49, No. 10, 105301

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We introduce a 3D model, and we study its stability, consisting of two distinct pairs of identical fermions coupled with a two-body interaction between fermions of different species, whose effective range is essentially zero (a so called (2+2)-fermionic system with zero-range interaction). The interaction is modelled by implementing the celebrated (and ubiquitous in the literature of this field) Bethe-Peierls contact condition with given two-body scattering length within the Krein-Visik-Birman theory of extensions of semi-bounded symmetric operators, in order to make the Hamiltonian a well-defined (self-adjoint) physical observable. After deriving the expression for the associated energy quadratic form, we show analytically and numerically that the energy of the model is bounded below, thus describing a stable system.

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