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 .

Phenomena such as pulsar frequency glitches are believed to be attributable to differential rotation of a current of "free" superfluid neutrons at densities above the "drip" threshold in the ionic crust of a neutron star. Such relative flow is shown to be locally describable by adaption of a canonical two fluid treatment that emphasizes the role of the momentum covectors constructed by differentiation of action with respect to the currents, with allowance for stratification whereby the ionic number current may be conserved even when the ionic charge number Z is altered by beta processes. It is demonstrated that the gauge freedom to make different choices of the chemical basis determining which neutrons are counted as "free" does not affect their "superfluid" momentum covector, which must locally have the form of a gradient (though it does affect the "normal" momentum covector characterising the protons and those neutrons that are considered to be "confined" in the nuclei). It is shown how the effect of "entrainment" (whereby the momentum directions deviate from those of the currents) is controlled by the (gauge independent) mobility coefficient K , estimated in recent microscopical quantum mechanical investigations, which suggest that the corresponding (gauge dependent) "effective mass" m ⋆ of the free neutrons can become very large in some layers. The relation between this treatment of the crust layers and related work (using different definitions of "effective mass") intended for the deeper core layers is discussed.

This is the first of a series of articles showing how 4 dimensionally covariant analytical procedures developed in the context of General Relativity can be usefully adapted for application in a purely Newtonian framework where they provide physical insights (e.g. concerning helicity currents) that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. After an introductory presentation of the relevant Milne spacetime structure and the associated Cartan connection, the essential principles are illustrated by application to the variational formulation of simple barotropic perfect fluid models. This variational treatment is then extended to conservative multiconstituent self gravitating fluid models of the more general kind that is needed for treating the effects of superfluidity in neutron stars.

The 4-dimensionally covariant approach to multiconstituent Newtonian fluid dynamics presented in the preceding article of this series is developed by construction of the relevant 4-dimensional stress energy tensor whose conservation in the non-dissipative variational case is shown to be interpretable as a Noether identity of the Milne spacetime structure. The formalism is illustrated by the application to homogeneously expanding cosmological models, for which appropriately generalised local Bernouilli constants are constructed. Another application is to the Iordanski type generalisation of the Joukowski formula for the Magnus force on a vortex. Finally, at a global level, a new (formally simpler but more generally applicable) version of the "virial theorem" is obtained for multiconsituent -neutron or other -fluid star models as a special case within an extensive category of formulae whereby the time evolution of variously weighted mass moment integrals is determined by corresponding space integrals of stress tensor components, with the implication that all such stress integrals must vanish for any stationary equilibrium configuration.

The buildup of the stress whose relaxation is presumed to account for pulsar frequency glitches can be attributed to various mechanisms, of which the most efficient involve differential rotation of the neutron superfluid in the inner layers of the (magnetically braked) solid crust of a rotating neutron star. In such a case it is usually supposed that the stress is attributable to pinning of superfluid vortices to crust nuclei, but it has been suggested that, even if the pinning effect is too weak, a comparably large stress might still arise just from the deficit of centrifugal buoyancy in the slowed down crust. The present work is a re-examination that investigates the way such processes may be affected by considerations that were overlooked in the previous work -notably uncertainties about the 'effective' masses that have to be attributed to the 'free' superfluid neutrons to allow for their entrainment by the ionic crust material. Though restricted to a Newtonian formulation, this analysis distinguishes more carefully than has been usual between true velocities, which are contravariantly vectorial, and so called 'superfluid velocities' that are proportional to momenta, which are essentially covectorial, a technicality that is important when more than one independent current is involved. The results include a Proudman-type theorem to the effect that the superfluid angular velocity must be constant on slightly deformed Taylor cylinders in the force free case, and it is shown how to construct a pair of integral constants of the motion that determine the solution for the pinned case assuming beta equilibrium.