Protons in High Density Neutron Matter

Abstract

We discuss the possible implication of the recent predictions of two new properties of high momentum distribution of nucleons in asymmetric nuclei for neutron star dynamics. The first property is about the approximate scaling relation between proton and neutron high momentum distributions weighted by their relative fractions ($x_p$ and $x_n$) in the nucleus. The second is the existence of inverse proportionality of the high momentum distribution strength of protons and neutrons to $x_{p/n}$. Based on these predictions we model the high momentum distribution functions for asymmetric nuclei and demonstrate that it describes reasonably well the high momentum characteristics of light nuclei. We also extrapolate our results to heavy nuclei as well as infinite nuclear matter and calculate the relative fractions of protons and neutrons with momenta above $k_{F}$. Our results indicate that for neutron stars starting at {\em three} nuclear saturation densities the protons with $x_p = {1\over 9}$ will populate mostly the high momentum tail of the momentum distribution while only $2\%$ of the neutrons will do so. Such a situation may have many implications for different observations of neutron stars which we discuss.