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 time-dependent dynamics of neutron star matter, which allows us to explore diverse properties of nuclear matter, including the entrainment effect. 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. *shortened due to the arXiv's word limit.

19 pages, 10 figures, 3 tables; v2 - A figure (Fig. 10) has been added. Version accepted for publication in Physical Review C

References in corpus (13)

• Models of Pulsar Glitches
• Neutron conduction in the inner crust of a neutron star in the framework of the band theory of solids
• Crustal Entrainment and Pulsar Glitches
• TDHF Theory and Its Extensions for the Multinucleon Transfer Reaction: a Mini Review
• On the validity of the Wigner-Seitz approximation in neutron star crust
• Low-energy collective excitations in the neutron star inner crust
• Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter
• Entrainment in Superfluid Neutron Star Crusts: Hydrodynamic Description and Microscopic Origin
• Nuclear Pasta Matter for Different Proton Fractions
• Nucleus--nucleus interactions in the inner crust of neutron stars
• Entrainment effects in neutron-proton mixtures within the nuclear-energy density functional theory. I. Low-temperature limit
• Properties of a quantum vortex in neutron matter
• Anderson-Bogoliubov phonon in inner crust of neutron stars: Dipole excitation in spherical Wigner-Seitz cell

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• Superfluid density in linear response theory : pulsar glitches from the inner crust of neutron stars
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