Abstract
We give a lower bound on the ground state energy of a system of two fermions of one species interacting with two fermions of another species via point interactions. We show that there is a critical mass ratio m2 ≈ 0.58 such that the system is stable, i.e., the energy is bounded from below, for m in [m_{2}, m_{2}^{-1}]. So far it was not known whether this 2 + 2 system exhibits a stable region at all or whether the formation of four-body bound states causes an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our result gives further evidence for the stability of the more general N + M system.
Highlights
1 Introduction Systems of particles interacting via point interactions are frequently used in physics to model short range forces
Point interactions were introduced in the 1930s to model nuclear interactions [4, 5, 12, 23, 24], and later they were successfully applied to other areas of physics like polarons or cold atomic gases [25]
The case N = M = 1 is completely understood as it reduces to a one particle problem [1]. In this case there exists a one-parameter family of Hamiltonians describing point interactions parameterized by the inverse scattering length, and they are bounded from below for all masses
Summary
Systems of particles interacting via point interactions are frequently used in physics to model short range forces.
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