  We study the localization of protons in the core of neutron stars for ten
realistic nuclear models that share a common behaviour of nuclear symmetry
energy which saturates and eventually decreases at high densities. This results
in the low proton fraction of beta-stable neutron star matter. Protons form a
small admixture in the neutron star core, which is localized at sufficiently
high densities. For every model we calculate the density $n_{loc}$ above which
the localization effect is present. Our results indicate that localization
occurs at densities above $0.5-1.0 fm^{-3}$. The phase with localized protons
occupies a spherical shell or a core region inside neutron stars which contains
significant fraction of all nucleons. Proton localization is of great
importance for astrophysical properties of neutron stars as it strongly affects
transport coefficients of neutron star matter and can produce spontaneous
magnetization in neutron stars.
