A neutron star formed in gravitational collapse of a stellar core (§ 1.4.2) is initially very hot, with the internal temperature ~ 1011 K. At such high temperatures, the composition and equation of state of the envelope of the newly-born star (p < 1014 g cm-3, nb < 0.1 fm-3) is different from that of the older star. This envelope will eventually become the neutron star crust.
In what follows, we will restrict ourselves to the case in which matter is transparent to neutrinos; this condition is satisfied for T < 1010 K (kBT < 1 MeV). The hot envelope is then a mixture of heavy and light atomic nuclei (mostly a-particles, because of their large binding energy of 28.3 MeV), neutrons, protons, electrons, positrons, and photons. At high densities and temperatures the density of nucleons outside nuclei can be large, and a consistent treatment of both nuclei and nucleons is required. The nuclei and the outside nucleons should be described using the same nucleon interaction (nucleon Hamiltonian). Modifications of the nuclear surface properties and pressure exerted by the nucleons on the nuclei have to be calculated in a consistent way. At high densities, where the distance between the nuclei becomes comparable to the nuclear size, one should also modify the nuclear Coulomb energy. Another important complication is that, at the temperatures under consideration, excited states of the nuclei become populated and must therefore be taken into account while calculating thermodynamic quantities.
All these effects have been incorporated in models of dense, hot matter using three different approaches. First, full Hartree-Fock calculations with an effective nucleon-nucleon (NN) interaction, for unit cells of matter containing one nucleus, were performed by Bonche & Vautherin (1981) and Wolff (1983). Second, finite temperature Thomas-Fermi calculations have been done by Marcos et al. (1982) and Ogasawara & Sato (1983). Third, calculations in which the nuclei have been described using the finite temperature compressible liquid-drop model have been performed by Lattimer et al. (1985).
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