Bound states of four identical bosons in two dimensions

Abstract

Within the framework of integral equations, the bound-state energies of tetramers in two spatial dimensions are determined for simple potential models. The equations are solved by using unitary pole expansions for the subamplitudes. Evidence is given for the coincidence of the thresholds of the binding of the $n$-particle system with $n=2, 3, \mathrm{and} 4$. For the class of potentials studied, it is found that the ratio between the tetramer and trimer binding energies is, to a good approximation, given by 2.9. Using this result, an estimate is given for the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ tetramer binding energy.