Geometrical packing and the solidification of neutron-star matter

We examine the role, if any, of geometrical packing or "caging" of the neutron repulsive cores in the solidification of neutron matter at neutron-star densities. A search for a stable solid phase retaining only the repulsive part of the Reid ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ potential and Bose statistics shows that this model system cannot sustain a solid core until densities much beyond 2 ${\mathrm{fm}}^{-3\mathrm{}}$. This indicates that the $n-n$ repulsive core is too soft to induce solidification at neutron-star densities. Using the analogy of helium it is argued that including the intermediate-range attractive well of the $n-n$ potential would not lower the solidification density significantly. In support of this, a second search was conducted with a potential which was a density-dependent average of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ Reid potentials (including the attractive part). Again no stable solid solution was found.