Few-body universality in the deuteron-alpha system

We treat ${}^6$Li as an effective three-body ($n$-$p$-$\alpha$) system and compute the $d$-$\alpha$ $S-$wave scattering length and three-body separation energy of ${}^6$Li for a wide variety of nucleon-nucleon and $\alpha$-nucleon potentials which have the same (or nearly the same) phase shifts. The Coulomb interaction in the $p$-$\alpha$ subsystem is omitted. The results of all calculations lie on a one-parameter curve in the plane defined by the $d$-$\alpha$ $S-$wave scattering length and the amount by which ${}^6$Li is bound with respect to the $n$-$p$-$\alpha$ threshold. We argue that these aspects of the $n$-$p$-$\alpha$ system can be understood using few-body universality and that ${}^6$Li can thus usefully be thought of as a two-nucleon halo nucleus.