Universal description of three two-component fermions

Abstract

A quantum-mechanical three-body problem for two identical fermions of mass m and a distinct particle of mass m1 in the universal limit of zero-range two-body interaction is studied. For the unambiguous formulation of the problem in the interval ( and ) an additional parameter b determining the wave function near the triple-collision point is introduced; thus, a one-parameter family of self-adjoint Hamiltonians is defined. The dependence of the bound-state energies on m/m1 and b in the sector of angular momentum and parity is calculated and analysed with the aid of a simple model.