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Proton fraction in the inner neutron-star crust

Monte Carlo simulations of neutron-rich matter of relevance to the inner neutron-star crust are performed for a system of A=5,000 nucleons. To determine the proton fraction in the inner crust, numerical simulations are carried out for a variety of densities and proton fractions. We conclude---as others have before us using different techniques---that the proton fraction in the inner stellar crust is very small. Given that the purported "nuclear pasta" phase in stellar crusts develops as a consequence of the long-range Coulomb interaction among protons, we question whether pasta formation is possible in such proton-poor environments. To answer this question, we search for physical observables sensitive to the transition between spherical nuclei and exotic pasta structures. Of particular relevance is the static structure factor S(k)---an observable sensitive to density fluctuations. However, no dramatic behavior was observed in S(k). We regard the identification of physical observables sensitive to the existence---or lack-thereof---of a pasta phase in proton-poor environments as an open problem of critical importance.