Nuclear shapes in the inner crust of a neutron star

Nuclear shapes in the inner crust of a neutron star are studied with due consideration for nuclear surface diffuseness and lattice types. The nuclear shapes considered are cylinder, slab and cylindrical hole in addition to sphere and spherical hole. The Thomas-Fermi calculations are performed in the zero-temperature approximation with four energy density functionals. These functionals are constructed so as to reproduce gross properties of laboratory nuclei and to be consistent with the equation of state of pure neutron matter by Friedman and Pandharipande. The nucleon distributions are parametrized in a way that allows a neutron gas outside the nuclei as well as different nuclear surfaces for neutrons and protons. This study confirms the liquid-drop result that the nuclear shape changes from sphere to cylinder, slab, cylindrical hole and spherical hole successively as the matter density increases. These shape changes occur at densities between 1.0 × 1014 and 1.5 × 1014 g/cm3, and are accompanied by first-order phase transitions. The density range for each nuclear shape to exist stably becomes narrower successively in the above order. At a fixed matter density, the energy difference between the phases of two successive nuclear shapes is of the order of 0.1–1 keV per nucleon. The existence of non-spherical nuclear shapes reduces the energy by an amount up to 3–5 keV per nucleon compared with the case in which only spherical and spherical hole nuclei are considered. This energy reduction corresponds to 4–6 MeV per spherical nucleus.