Cluster Expansion of Cold Alpha Matter Energy

TL;DR

This paper analytically calculates the contributions of two, three, and four-body interactions to the ground state energy of infinite cold alpha matter using a cluster expansion approach with Gaussian correlations.

Contribution

It provides explicit analytical expressions for multi-body diagrams in alpha matter and demonstrates rapid convergence of the cluster expansion with realistic potentials.

Findings

Four-body contributions are significantly smaller than two- and three-body contributions.

The cluster expansion converges rapidly under the assumptions made.

Analytical expressions are derived for multi-body diagrams in alpha matter.

Abstract

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.