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.Comment: 8 pages, 4 figure

Cluster Expansion of Cold Alpha Matter Energy

In the cluster expansion framework of Bose liquids we calculate analytical expressions of the two-body, three-body and four-body diagrams contributing to the g.s. energy of an infinite system of neutral alpha-particles at zero-temperature, interacting via the strong nuclear forces exclusively. This is analytically tractable by assuming a density dependent two-body correlation function of Gaussian type. For the alpha-alpha potential we adopt the phenomenological Ali-Bodmer interaction and semi-microscopic potentials obtained from the Gogny force parametrizations. We show that under such assumptions we achieve a rapid convergence in the cluster expansion, the four-body contributions to the energy being smaller than the two-body and three-body contributions by at least an order of magnitude.Comment: 22 pages, 13 figure