Inner crusts of neutron stars in strongly quantising magnetic fields

We study the properties and stability of nuclei in the inner crust of neutron stars in the presence of strong magnetic fields $\sim 10^{17}$ G. Nuclei coexist with a neutron gas and reside in a uniform gas of electrons in the inner crust. This problem is investigated within the Thomas-Fermi model. We extract the properties of nuclei based on the subtraction procedure of Bonche, Levit and Vautherin. The phase space modification of electrons due to Landau quantisation in the presence of strong magnetic fields leads to the enhancement of electron as well as proton fractions at lower densities $\sim 0.001$ fm$^{-3}$. We find the equilibrium nucleus at each average baryon density by minimising the free energy and show that, in the presence of strong magnetic fields, it is lower than that in the field free case. The size of the spherical cell that encloses a nucleus along with the neutron and electron gases becomes smaller in strong magnetic fields compared with the zero field case. Nuclei with larger mass and atomic numbers are obtained in the presence of strong magnetic fields as compared with cases of zero field.