Binding properties of the (2+1)-fermion system with zero-range interspecies interaction

We study analytically and numerically the binding properties, in particular the ground state, of the so-called (2+1)-fermion system, which is a three-dimensional system of two identical fermions interacting with a third particle of different species through a zero-range interaction. We model the system with a specific self-adjoint point interaction Hamiltonian recently constructed in the mathematical literature. First we characterize the internal symmetry of the bound states in the attractive case. Then we show that the system confines in a precise regime of masses and that its ground-state energy stays finite as the mass becomes close to the critical point of the collapse of the system. © 2013 American Physical Society.