dorsal/arxiv
View SchemaEntrainment coefficient and effective mass for conduction neutrons in neutron star crust: simple microscopic models
| Authors | Brandon Carter, Nicolas Chamel, Pawel Haensel |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0402057 |
| URL | https://arxiv.org/abs/nucl-th/0402057 |
| DOI | 10.1016/j.nuclphysa.2004.11.006 |
| Journal | Nucl. Phys. A748 (2005) 675-697 |
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 $n^i= n \bar v^i$ of such conduction neutrons will be related to the corresponding mean particle momentum $p_i$ by a proportionality relation of the form $n^i= {\cal K}p^i$ in terms of a physically well defined mobility coefficient $\cal K$ 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 $\cal K$ 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 $m_\star=n/{\cal K}$. 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 $m_\star$ will become very large compared with m.
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"abstract": "In the inner crust of a neutron star, at densities above the ``drip\u0027\u0027\nthreshold, unbound ``conduction\u0027\u0027 neutrons can move freely past through the\nionic lattice formed by the nuclei. The relative current density $n^i= n \\bar\nv^i$ of such conduction neutrons will be related to the corresponding mean\nparticle momentum $p_i$ by a proportionality relation of the form $n^i= {\\cal\nK}p^i$ in terms of a physically well defined mobility coefficient $\\cal K$\nwhose value in this context has not been calculated before. Using methods from\nordinary solid state and nuclear physics, a simple quantum mechanical treatment\nbased on the independent particle approximation, is used here to formulate\n$\\cal K$ as the phase space integral of the relevant group velocity over the\nneutron Fermi surface. The result can be described as an ``entrainment\u0027\u0027 that\nchanges the ordinary neutron mass m to a macroscopic effective mass per neutron\nthat will be given -- subject to adoption of a convention specifying the\nprecise number density n of the neutrons that are considered to be ``free\u0027\u0027 --\nby $m_\\star=n/{\\cal K}$. The numerical evaluation of the mobility coefficient\nis carried out for nuclear configurations of the ``lasagna\u0027\u0027 and ``spaghetti\u0027\u0027\ntype that may be relevant at the base of the crust. Extrapolation to the middle\nlayers of the inner crust leads to the unexpected prediction that $m_\\star$\nwill become very large compared with m.",
"arxiv_id": "nucl-th/0402057",
"authors": [
"Brandon Carter",
"Nicolas Chamel",
"Pawel Haensel"
],
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"nucl-th",
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"doi": "10.1016/j.nuclphysa.2004.11.006",
"journal_ref": "Nucl. Phys. A748 (2005) 675-697",
"title": "Entrainment coefficient and effective mass for conduction neutrons in neutron star crust: simple microscopic models",
"url": "https://arxiv.org/abs/nucl-th/0402057"
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