Effective field theory for the Helium-6 halo nucleus

The ground-state of Helium-6 can be treated as a two-neutron halo with an alpha-particle core. This bound state is generated by the resonant $nn$ and $n\alpha$ interactions. The latter is dominated by a shallow p-wave resonance, where both the scattering length and effective range appear at leading order [1]. Here we first study a separable-potential model which fits the $nn$ and $n\alpha$ scattering parameters (c.f., e.g. [2]). This reproduces known properties of He-6 moderately well for a specific choice of interaction ranges. We then show that the He-6 binding energy diverges in the limit that the range of the $n \alpha$ and $nn$ forces goes to zero. This indicates that within Halo EFT this three-body system needs an $nn \alpha$ contact interaction to be properly renormalized at leading order. We adjust the coefficient of this $nn \alpha$ force to reproduce the Helium-6 ground-state energy, and present its running as a function of the cutoff. The correlations amongst Helium-6 properties that result from this successful renormalization of the leading-order three-body problem in halo EFT with p-wave resonant interactions will be discussed. \\[4pt] [1] C.~A.~Bertulani, {\it et al.}, Nucl.\ Phys.\ {\bf A712}, 37 (2002). \newline [2] A.~Ghovanlou, D.~R.~Lehman, Phys.\ Rev.\ {\bf C9}, 1730 (1974).