Bounds on the existence of neutron rich nuclei in neutron star interiors

We address the question concerning the maximum density, at which nuclei (and more generally -- nuclear structures) can exist in neutron star interiors. An absolute upper bound to such a density is obtained using the bulk approximation, in which surface and Coulomb effects are neglected. A very good approximation to the limiting density is given by the threshold for the instability of a uniform n-p-e plasma with respect to density modulations; this threshold is calculated using the Extended Thomas-Fermi approximation for the Skyrme energy functionals. For recent SLy Skyrme forces, which are particularly suitable for the description of very neutron rich nucleon systems, the maximum density at which nuclear structures can exist is 0.08 nucleons/fm^3 (i.e., half of the normal nuclear density); at this density protons constitute only 4\% of nucleons.