High-Density Nucleon Localization

A nucleon system interacting by means of the Reid soft-core potential is considered at the very high densities which would be found in the core regions of neutron stars. The question of nucleon localization is considered, first with a simple Wigner-type calculation and then with a variational calculation in which the degree of crystallization is used as a variational parameter. The conclusion is that for some range of densities between $r_0=0.2\mathrm{}$ F and $r_0=0.8\mathrm{}$ $\mathrm{F} (\frac{V}{N}=4\mathrm{}\pi \frac{{r_0}^3}{3})$ nucleons should localize in the sense that a crystal-like wave function which introduces particle anticorrelations by localizing the particles with respect to a periodic lattice is preferable to a plane-wave type of wave function which has only statistical correlations and that this is probably not true outside this region. There is no attempt to distinguish liquids from crystals, merely a gas from a crystal. The energy upper bounds resulting from the variational calculation are also given.