applied to the neutron star

The role of the boundary conditions in the Wigner-Seitz approximation applied to the neutron star inner crust. Abstract The influence of the boundary conditions used in the Wigner-Seitz approximation applied to the neutron star inner crust is examined. The generalized energy functional method which includes neutron and proton pairing correlations is used. Predictions of two versions of the boundary conditions are compared with each other. The uncertainties in the equilibrium configuration (Z, R c) of the crust, where Z is the proton charge and R c the radius of the Wigner-Seitz cell, correspond to variation of Z by 2 – 6 units and of R c , by 1 – 2 fm. The effect of the boundary conditions is enhanced at increasing density. These uncertainties are smaller than the variation of Z and R c coming from the inclusion of pairing. The value of the pairing gap itself, especially at high density, can depend on the boundary condition used. In the last two decades the interest on the structure of the neutron star inner crust has been stimulated by the increasing number of observational data on the pulsar glitches. The latter are commonly explained in terms of the dynamics of superfluid vortices within the inner crust of neutron stars (see [1] and Refs. therein). By " inner crust " one usually indicates the part of the shell of a neutron star with sub-nuclear densities 0.001ρ 0 ≤ ρ ≤ 0.5ρ 0 , where ρ 0 is the normal nuclear density. According to present-day ideas, the bulk of the inner crust consists mainly of spherically symmetrical nuclear-like clusters which form a crystal matrix immersed in a sea of neutrons and virtually uniform sea of electrons. Such a picture was first justified microscopically in the classical paper by Negele and Vautherin (NV) [2] within the Wigner-Seitz (WS) approximation. Up to now, the WS method remains to be quite popular in this field. Only recently a more consistent band theory was developed for the deep (high density) layers [3], where the " lasagna " or " spaguetti " structure of the crust matter is supposed to be favored, and for 1