SHELL ENERGIES OF NONSPHERICAL NUCLEI IN THE INNER CRUST OF A NEUTRON-STAR

Shell effects in the non-spherical nuclei, which may exist in the inne r crust of a neutron star, are studied. Spherical as well as non-spher ical single-particle potentials are constructed based on the results o f Thomas-Fermi calculations. In order to take into account the spin-or bit forces and the finite-range effects of nuclear interactions, three parameters are introduced in these potentials and their values are de termined so as to be consistent with the single-particle energies in n ormal nuclei. Shell energies of the non-spherical nuclei are extracted from the single-particle energies in the non-particle potentials. Neu tron-shell energies are found to be negligibly small compared with pro ton-shell energies, and the band-structure effects of protons are also very small at the densities of interest, (1.0 - 1.5) x 10(14) g/cm3. The proton-shell energies are found to be somewhat smaller than the en ergy difference between the successive nuclear shapes. Numerical calcu lations are performed for spherical, cylindrical and slab-shape nuclei while for cylindrical-hole and spherical-hole nuclei an argument is g iven that the shell effects are expected to be small. Therefore, we co nclude that the shell effects do not change the qualitative features o f the Thomas-Fermi results; namely, as the average matter density incr eases from subnuclear to normal nuclear density, the stable nuclear sh ape changes successively from sphere to cylinder, slab, cylindrical ho le and spherical hole before going into uniform matter. Quantitatively , however, the shell effects cause some change; the transitions from s phere to cylinder and from cylinder to slab occur at somewhat higher d ensities than in the Thomas-Fermi calculation.