Universal Behavior of Few-Boson Systems Using Potential Models
Résumé
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 $\kappa _*$ and the two-body scattering length a, $\kappa _* a$ depends on the angle $\xi $ defined by $E_3/E_2=\tan ^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$^4$ He atoms.