Alpha matter revisited

We examine in detail two alternative descriptions of a system of $\alpha$ particles interacting via local interactions of different character, highlighting the fact that a faithful microscopic description of such systems demands a consistent treatment of both short- and long-range correlations. In preparation, we examine four different versions of modern microscopic many-body theory and conclude by emphasizing that these approaches, although {\it a priori} very different, actually lead to the same equations for their efficient application. The only quantity that depends on the formulation of many-body theory chosen is an {\it irreducible} interaction correction. In the language of Green's functions and Feynman diagrams, it is the set of both particle-particle and particle-hole irreducible diagrams, and in variational Jastrow-Feenberg theory it is determined by {\it multipartite correlations} and {\it elementary diagrams}. We apply these theoretical methods to the calculation of the energetics, structure, thermodynamics, and dynamics of $\alpha$ matter, as well as its condensate fraction. In dimensionless units, $\alpha$ matter appears to be remarkably similar to the much-studied $^4$He quantum fluid, its low-temperature properties now basically solved in the Jastrow-Feenberg framework. Accordingly, one can have confidence in the results of application of the same procedure to $\alpha$ matter. Even so, closer examination reveals significant differences between the physics of the two systems. Within an infinite nuclear medium, alpha matter is subject to a spinoidal instability. Extended mixtures of nucleons and alpha particles are yet to be given rigorous consideration in a corresponding theoretical framework.