Time-dependent extension of the self-consistent band theory for neutron star matter: Anti-entrainment effects in the slab phase

Abstract

Background: In the solid crust of neutron stars, a variety of crystalline structure may exist. Recently the band theory of solids has been applied to the inner crust of neutron stars and significance of the entrainment between dripped neutrons and the solid crust was advocated. Since it influences interpretations of various phenomena of neutron stars, it has been desired to develop deeper understanding of the microphysics behind.Purpose: The purpose of the present article is to propose a fully self-consistent microscopic framework for describing timedependent dynamics of neutron star matter, which allows us to explore diverse properties of nuclear matter, including the entrainment effect.Methods: A fully self-consistent nuclear band theory is employed with Skyrme SLy4 energy density functional. A timedependent extension of the microscopic band theory is developed based on the time-dependent density functional theory (TDDFT). An intuitive real-time method is proposed for extracting the collective mass of a nuclear cluster immersed in a sea of dripped neutrons.Results: As the first application of the time-dependent self-consistent band theory for nuclear systems, we investigate the slab phase of nuclear matter with various proton fractions. From a dynamic response of the system to an external force, we extract the collective mass of a slab, associated with entrained neutrons as well as bound nucleons. We find that the extracted collective mass is smaller than a naive estimation based on a potential profile and single-particle energies. We show that the reduction is mainly caused by "counterflow" of dripped neutrons towards the direction opposite to the motion of the slabs. We interpret it as an "anti-entrainment" effect. As a result, the number of effectively bound neutrons is reduced, indicating an enhancement of the number density of conduction neutrons. We demonstrate that those findings are consistent with a static treatment in the band theory of solids. Conclusions:The proposed approach offers a new research possibility of investigating non-linear many-body dynamics of nuclear matter microscopically, taking full account of the periodic structure in the neutron star crusts. The fully self-consistent band theory calculations, in both static and dynamic formalisms, suggest that the mobility of dripped neutrons is larger than expected without band structure effects, at least for the slab phase of nuclear matter.