Abstract
The poorly known crustal equation of state plays a critical role in many observational phenomena associated with a neutron star. Using semi-classical Monte Carlo simulations, we explore the possible configurations of the inner edge of the neutron-star crust for a variety of baryon densities and proton fractions. Applying the Kirkwood--Buff theory to these two-component systems, we observe how the isothermal compressibility reaches a maximum when isolated non-symmetric clusters are formed in an extremely dilute neutron gas. To determine the neutron fraction, we suggest a geometrical model based on the behavior of the proton-neutron pair correlation function. Accordingly, the equation of state of the inner crust is calculated, illustrating that the nuclear energy in beta-equilibrium follows a power-law behavior with baryon density. As a possible astrophysical outcome of this study, our results could help refine the mass-radius relation. Finally, our results pave the way towards further investigations of the impact of the proton-neutron pair correlation function on transport properties within the neutron-star crust.
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