Universal Properties of the Four-Boson System in Two Dimensions

We consider the nonrelativistic four-boson system in two dimensions interacting via a short-range attractive potential. For a weakly attractive potential with one shallow two-body bound state with binding energy B₂, the binding energies B_N of shallow N-body bound states are universal and thus do not depend on the details of the interaction potential. We compute the four-body binding energies in an effective quantum mechanics approach. There are exactly two bound states: the ground state with B₄⁽⁰⁾=197.3(1)B₂ and one excited state with B₄⁽¹⁾=25.5(1)B₂. We compare our results to recent predictions for N-body bound states with large N1.On leave from FZ Jülich, Institut für Kernphysik (Theorie), D-52425 Jülich and HISKP (Theorie), Universität Bonn, Nußallee 14–16, D-53115 Bonn, Germany