The Quantum Liquid of Alpha Clusters

Within the variational approach of Bose liquids we analyze the g.s. energy of charge neutral alpha matter at $T$=0. As a prerequisite for such calculation we take from the literature or propose new $\alp-\alp$ potentials that are particularly suitable for this task, i.e. posses a repulsive core and/or reproduce the low energy scattering data and the resonance properties of the $\alp-\alp$ system. The alpha matter EOS is then obtained with the HNC method using Pandharipande-Bethe correlation derived variationally in the lowest order expansion of the energy functional or a simple gaussian function with a healing range determined by the normalization of the radial distribution function in the lowest order. We show that saturation is achieved only via repulsive and shallow potentials that are not consistent with the scattering and resonance constraints.