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

Abstract

Background: The inner crust of neutron stars consists of a Coulomb lattice of neutron-rich nuclei, immersed in a sea of superfluid neutrons with background relativistic electron gas. A proper quantum mechanical treatment for such a system under a periodic potential is the band theory of solids. The effect of band structure on the effective mass of dripped neutrons, the so-called \textit{entrainment effect}, is currently in a debatable situation, and it has been highly desired to develop a nuclear band theory taking into account neutron superfluidity in a fully self-consistent manner. Purpose: The main purpose of the present work is twofold: 1) to develop a formalism of the time-dependent self-consistent band theory, taking full account of nuclear superfluidity, based on time-dependent density functional theory (TDDFT) extended for superfluid systems, and 2) to quantify the effects of band structure and superfluidity on crustal properties, applying the formalism to the slab phase of nuclear matter in the $\beta$ equilibrium. Results: Static calculations have been performed for a range of baryon (nucleon) number density ($n_b=0.04-0.07$ fm${}^{-3}$) under the $\beta$-equilibrium condition with and without superfluidity, for various inter-slab spacings. From a dynamic response to an external potential, we extract the collective mass of a slab and that of protons immersed in neutron superfluid. From the results, we find that the collective mass of a slab is substantially reduced by 57.5--82.5\% for $n_b=0.04-0.07$ fm${}^{-3}$, which corresponds to an enhancement of conduction neutron number density and, thus, to a reduction of the neutron effective mass, which we call the anti-entrainment effect. We discuss novel phenomena associated with superfluidity, quasiparticle resonances in the inner crust, which are absent in normal systems. *shortened due to the arXiv word limit.

21 pages, 11 figures, 4 tables. v4 - Version accepted for publication in Physical Review C, selected as an Editors' Suggestion

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• Superfluid density in linear response theory : pulsar glitches from the inner crust of neutron stars
• Superfluid fraction in the crystalline crust of a neutron star: role of BCS pairing
• Time-dependent nuclear energy-density functional theory toolkit for neutron star crust: Dynamics of a nucleus in a neutron superfluid
• Superfluid fraction in the rod phase of the inner crust of neutron stars
• Emergence of the geometric contribution to the superfluid density in the inner crust of neutron stars
• Phase transitions in the inner crust of neutron stars within the superfluid band theory: Competition between ${}^1{\text{S}}_0$ pairing and spin polarization under finite temperature and magnetic field
• Fermi Operator Expansion for the Hartree-Fock-Bogoliubov Theory
• Local Quantum Cooling for Large Fermi Systems with Pairing
• Superfluid fraction in the crystalline crust of a neutron star: role of quantum zero-point motion of ions