Universal behavior of few-boson systems using potential models

Abstract: The universal behavior of a three-boson system close to the unitary limit is encoded in a simple dependence of many observables in terms of few parameters. For example the product of the three-body parameter $\kappa_<em>$ and the two-body scattering length $a$, $\kappa_</em> a$ depends on the angle $\xi$ defined by $E_3/E_2=\tan<sup>2\xi$. A similar dependence is observed in the ratio $a_{AD}/a$ with $a_{AD}$ the boson-dimer scattering length. We use a two-parameter potential to determine this simple behavior and, as an application, to compute $a_{AD}$ for the case of three $<sup>4$He atoms.