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

Brandon Carter; Nicolas Chamel; Pawel Haensel

doi:10.1016/j.nuclphysa.2004.11.006

paper

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

arXiv:nucl-th/0402057 · doi:10.1016/j.nuclphysa.2004.11.006

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 $n^{i} = n v ˉ^{i}$ of such conduction neutrons will be related to the corresponding mean particle momentum $p_{i}$ by a proportionality relation of the form $n^{i} = K p^{i}$ 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.

arXiv comment27 pages, latex. Revised published version

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

Abstract

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