Nuclear band theory of neutron star crust
The inner crust of a neutron star is formed of a crystal lattice
of nuclear clusters immersed in a neutron sea. This nuclear environment
is closely analogous to more familiar periodic systems in condensed
matter, like for instance electrons in ordinary metals, atomic Bose
gases in optical lattices, photonic or phononic crystals. All these
periodic systems are described by the band theory of solids developed
by Felix Bloch.
I started a few years ago to adapt for the first time this theory to
neutron star crust. The band theory allows a consistent treatment of
both the free neutrons and the nucleons bound inside nuclear clusters.
The figure below shows an example of a numerical calculation of
the neutron band structure (left) and the corresponding Fermi surface
(right), at a density of 700 billion grams per cubic centimeters.
The crust is composed of a body centered cubic lattice of
zirconium like clusters (40 protons per lattice site). The different
colors are associated with different branches of the Fermi surface.
see Chamel, Nucl. Phys. A747(2005), 109. PDF
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