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3 The Ground State Structure of Neutron Star Crusts

According to the cold catalyzed matter hypothesis, the matter inside cold non-accreting neutron stars is assumed to be in complete thermodynamic equilibrium with respect to all interactions at zero temperature and is therefore supposed to be in its ground state with the lowest possible energy. The validity of this assumption is discussed in Section 3.4.

The ground state structure of a neutron star crust is sketched in Figure 4View Image. The outer crust (Section 3.1) consists of a body-centered cubic lattice of iron 56Fe. At ρ ∼ 104 g cm −3 the atoms are fully ionized owing to the high density. At densities above 107 g cm–3, the composition of the nuclei becomes more neutron rich as a result of electron captures. The inner crust (Section 3.2), which extends from ρND ≃ 4 × 1011 g cm − 3 to ∼ ρ0∕3 ≃ 1014 g cm− 3, is characterized by the presence of free neutrons, which may condense into a superfluid phase in some layers (see Section 8). At the bottom of the crust, some calculations predict various “pasta” phases of non-spherical nuclei, such as slabs or cylinders as discussed in Section 3.3.

The ground state of a neutron star crust is obtained by minimizing the total energy density ɛtot for a given baryon density nb under the assumption of β-equilibrium and electric charge neutrality. For simplicity, the crust is assumed to be formed of a perfect crystal with a single nuclear species at lattice sites (see Jog & Smith [221Jump To The Next Citation Point] and references therein for the possibility of heteronuclear compounds).

View Image

Figure 4: Schematic picture of the ground state structure of neutron stars along the density axis. Note that the main part of this figure represents the solid crust since it covers about 14 orders of magnitude in densities.
 3.1 Structure of the outer crust
 3.2 Structure of the inner crust
  3.2.1 Liquid drop models
  3.2.2 Semi-classical models
  3.2.3 Quantum calculations
  3.2.4 Going further: nuclear band theory
 3.3 Pastas
 3.4 Impurities and defects

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