Entrainment coefficient and effective mass for conduction neutrons in neutron star crust: simple microscopic models

Abstract

Abstract. In the inner crust of a neutron star, at densities above the "drip" threshold, unbound "conduction" neutrons can move freely past through the ionic lattice formed by the nuclei. The relative current density n i = nv i of such conduction neutrons will be related to the corresponding mean particle momentum p i by a proportionality relation of the form n i = Kp i in terms of a physically well defined mobility coefficient K whose value in this context has not been calculated before. Using methods from ordinary solid state and nuclear physics, a simple quantum mechanical treatment based on the independent particle approximation, is used here to formulate K as the phase space integral of the relevant group velocity over the neutron Fermi surface. The result can be described as an "entrainment" that changes the ordinary neutron mass m to a macroscopic effective mass per neutron that will be given -subject to adoption of a convention specifying the precise number density n of the neutrons that are considered to be "free" -by m ⋆ = n/K . The numerical evaluation of the mobility coefficient is carried out for nuclear configurations of the "lasagna" and "spaghetti" type that may be relevant at the base of the crust. Extrapolation to the middle layers of the inner crust leads to the unexpected prediction that m ⋆ will become very large compared with m .

Effect of BCS pairing on entrainment in neutron superfluid current in neutron star crust

“…in which the interaction termĤ int will be absent in the independent particle limit corresponding to the kind of model used [6] in our preceding first quantised treatment.…”

“…Since (particularly for the middle layers of a neutron star crust, where the effective mass enhancement is likely [6,7] to be most important) we are still far from having a sufficient knowledge of the solutions ϕ kα {r} for the independent particle model, it will evidently take some time before we can hope to obtain a complete evaluation of the solutions for the coupled equations for ϕ 0 kα {r} and ϕ 1 kα {r} using an accurate estimate of the coupling coefficient ∆{r} . In the meanwhile, as an immediately available approximation, offering the best that can be hoped for as a provisional estimate in the short run, we can use an ansatz of the standard BCS kind, which means adopting the prescription U kα,lβ = cos θ kα δ kl δ αβ , V kα,lβ = sin θ kα δ −k,l δ αβ .…”

“…The salient conclusion to be drawn from all this work is that in these homogeneous fluid layers the effective mass of the neutron will be significantly but not enormously reduced (by several tens of percent) below its ordinary bare mass value. The present article is part of a newer program of work [6,7] concerned with the previously unstudied problem of evaluating what turns out to be a much more substantial effective mass modification that is obtained from the corresponding entrainment coefficients in the crust at subnuclear densities, above the neutron drip threshold (at about 10 11 g/cm 3 ). In these layers, relativistic corrections are insignificant but the issue is complicated by the microscopic inhomogeneity of the medium, in which some neutrons can still flow freely but protons are confined to atomic nuclei.…”

Low-energy collective excitations in the neutron star inner crust

“…[5]). Despite the absence of viscous drag, the neutron superfluid can still be coupled to the crust due to non-dissipative entrainment effects arising from elastic Bragg scattering of dripped neutrons by the crystal lattice [6,7]. Recent calculations have shown that in some regions of the inner crust only a very small fraction of dripped neutrons participate in the superfluid dynamics [8,9].…”

Band structure effects for dripped neutrons in neutron star crust

“…In a preceeding work [1,2] we have introduced a macroscopic effective mass m ⋆ relevant for hydrodynamical simulations, such that the momentum of the neutron superfluid is given by the mean neutron velocity times this effective mass in the crust rest frame. In a (super)fluid mixture, in general the momentum of one species is a linear combination of the particle currents of the other components.…”