Exploring the Drip Point in Neutron Stars via a Modified Semi-Empirical Mass Formula

The realistic case of nuclei, rather than free protons, capturing the electrons is investigated by extrapolating the semi-empirical mass formula of nuclei to the case of neutron-rich nuclei.  Beyond a critical density new neutrons produced by capture can not form bound states with the nuclei and drip out. The neutron drip transition is crucial for determining the crustal composition and have been investigated by using several approaches in the literature. These approaches confirm that the transition is highly sensitive to the semi-empirical mass formula which determines the binding energy of the nuclei. To determine the
crustal composition a modified version of the semi-empirical mass formula, obtained by a genetic algorithm rather than a Bayesian neural network or any other method, is employed. This version of the mass formula involves a modification of the liquid drop model by considering an asymmetry and deformation of the nucleons at the limit of stability and adds extra terms to the surface energy, $-a_{s}A^{2/3}$. 
The narrowing of the valley of stability, revealing a shift in the neutron drip line to lower mass numbers and an increase in neutron drip density, is investigated. Recent results in the context of displacive ferroelectric materials such as BaTiO$_3$ are discussed for the possible compositions of the neutron star crusts.