A Thomas-Fermi model of localization of proton impurities in neutron matter

Abstract

We show that the proton impurity in a neutron matter can create an inhomogeneity in density which acts as a potential well localizing the proton’s wave function. At low densities this inhomogeneity is a neutron bulge, whereas at high densities a neutron deficiency (bubble) occurs. We calculate variationally the proton’s energy using a Gaussian wave function. The neutron background is treated in a Thomas–Fermi approximation. The Skyrme interactions are used. We find that the localized proton has lower energy than the plane wave proton for densities below the lower critical density n$_{1} \cong$ 0.3n$_{0}$, and above the upper critical density n$_{u} \cong$ 2.2n$_{0}$, where n$_{0}$ = 0.17 fm$^{-3}$. We discuss some implications of the proton localization for magnetic properties of neutron matter containing a small admixture of protons