Entrainment effects in neutron-proton mixtures within the nuclear-energy density functional theory. I. Low-temperature limit

TL;DR

This paper investigates the entrainment effects in cold neutron-proton mixtures using nuclear energy-density functional theory, deriving exact expressions for mass currents and relating them to neutron star phenomena and finite nuclei.

Contribution

It provides a self-consistent derivation of mass currents and an analytical formulation of the entrainment matrix in terms of the isovector effective mass.

Findings

Derived exact expressions for mass currents in neutron-proton mixtures.

Established the equivalence with Fermi-liquid expressions.

Linked entrainment effects in neutron stars to isovector giant dipole resonances.

Abstract

Mutual entrainment effects in cold neutron-proton mixtures are studied in the framework of the self-consistent nuclear energy-density functional theory. Exact expressions for the mass currents, valid for both homogeneous and inhomogeneous systems, are directly derived from the time-dependent Hartree-Fock equations with no further approximation. The equivalence with the Fermi-liquid expression is also demonstrated. Focusing on neutron-star cores, a convenient and simple analytical formulation of the entrainment matrix in terms of the isovector effective mass is found, thus allowing to relate entrainment phenomena in neutron stars to isovector giant dipole resonances in finite nuclei. Results obtained with different functionals are presented. These include the Brussels-Montreal functionals, for which unified equations of state of neutron stars have been recently calculated.