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Nuclei in Strongly Magnetised Neutron Star Crusts

We discuss the ground state properties of matter in outer and inner crusts of neutron stars under the influence of strong magnetic fields. In particular, we demonstrate the effects of Landau quantization of electrons on compositions of neutron star crusts. First we revisit the sequence of nuclei and the equation of state of the outer crust adopting the Baym, Pethick and Sutherland (BPS) model in the presence of strong magnetic fields and most recent versions of the theoretical and experimental nuclear mass tables. Next we deal with nuclei in the inner crust. Nuclei which are arranged in a lattice, are immersed in a nucleonic gas as well as a uniform background of electrons in the inner crust. The Wigner-Seitz approximation is adopted in this calculation and each lattice volume is replaced by a spherical cell. The coexistence of two phases of nuclear matter - liquid and gas, is considered in this case. We obtain the equilibrium nucleus corresponding to each baryon density by minimizing the free energy of the cell. We perform this calculation using Skyrme nucleon-nucleon interaction with different parameter sets. We find nuclei with larger mass and charge numbers in the inner crust in the presence of strong magnetic fields than those of the zero field case for all nucleon-nucleon interactions considered here. However, SLy4 interaction has dramatic effects on the proton fraction as well as masses and charges of nuclei. This may be attributed to the behaviour of symmetry energy with density in the sub-saturation density regime. Further we discuss the implications of our results to shear mode oscillations of magnetars.