A microscopic hyper-spherical model: application to $^6$He

We have developed a microscopic cluster model of light two neutron halo nuclei that incorporates the few-body asymptotics in full extent. The wavefunction of the system consists of a core and two valence neutrons. The core is given in terms of correlated Gaussians. The three-body dynamics between the core and valence neutrons are taken into account by means of the hyper-spherical functions containing an exponentially decaying hyper-radial part. The center of mass motion is removed by construction. In this talk, we present the first results of our model applied to $^6$He. The central Minnesota N-N interaction with a spin-orbit addition is used to bind the system. Basic structural observables, such as binding relative to $^4$He, radii and one-body densities are in agreement with other microscopic calculations employing similar N-N interactions. The microscopic description of the core allows us to test the efficiency of Pauli projection techniques employed in the few-body models. We demonstrate that proper antisymmetrization is crucial to bind $^6$He against three-body break-up. We also present overlap functions between $^4$He and $^6$He with the aim of future reaction calculations.