Properties of dense nucleon matter and the structure of neutron stars are studied using variational chain summation methods and the new Argonne v 18 two-nucleon interaction, which provides an excellent fit to all of the nucleonnucleon scattering data in the Nijmegen data base. The neutron star gravitational mass limit obtained with this interaction is 1.67M ⊙ . Boost corrections to the two-nucleon interaction, which give the leading relativistic effect of order (v/c) 2 , as well as three-nucleon interactions, are also included in the nuclear Hamiltonian. Their successive addition increases the mass limit to 1.80 and 2.20 M ⊙ . Hamiltonians including a three-nucleon interaction predict a transition in neutron star matter to a phase with neutral pion condensation at a baryon number density of ∼ 0.2 fm −3 . Neutron stars predicted by these Hamiltonians have a layer with a thickness on the order of tens of meters, over which the density changes rapidly from that of the normal to the condensed phase. The material in this thin layer is a mixture of the two phases. We also investigate the possibility of dense nucleon matter having an admixture of quark matter, described using the bag model equation of state. Neutron stars of 1.4M ⊙ do not appear to have quark matter admixtures in their cores. However, the heaviest stars are predicted to have cores consisting of a quark and nucleon matter mixture. These admixtures reduce the maximum mass of neutron stars from 2.20 to 2.02 (1.91) M ⊙ for bag constant B = 200 (122) MeV/fm 3 . Stars with pure quark matter in their cores are found to be unstable. We also consider the possibility that matter is maximally incompressible above an assumed density, and show that realistic models of nuclear forces limit the maximum mass of neutron stars to be below 2.5M ⊙ . The effects of the phase transitions on the composition of neutron star matter and its adiabatic index Γ are discussed.PACS numbers: 21.65.+f, 26.60.+c, 97.60.Jd

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Over the past quarter of a century, the challenge of understanding the properties of neutron stars has been a powerful stimulus to studies of neutron-rich matter.This review considers neu tron-rich m�ltter at subnuclear densities. Under these conditions, the basic constituents of matter are neutrons, protons, and electrons, and their interactions are well characterized. In addition, theoretical many-body techniques are sufficiently well developed that properties of matter can be esti mated with a useful degree of precision. Among the topics addressed are the bulk and surface properties of neutron-rich matter, the prediction of nonspherical nuclei in neutron-star crusts, superf i uidity, departures from equilibrium, and the structure of the outer parts of neutron stars.

We calculate properties of neutron star matter at subnuclear densities using an improved nuclear Hamiltonian. Nuclei disappear and the matter becomes uniform at a density of about 0.6n s , where n 3 « 0.16 fm -3 is the saturation density of nuclear matter. As a consequence the mass of matter in the crusts of neutron stars is only about half as large as previously estimated. In about half of that crustal mass, nuclear matter occurs in shapes very different from the roughly spherical nuclei familiar at lower densities. The thinner crust and the unusual nuclear shapes have important consequences for theories of the rotational and thermal evolution of neutron stars, especially theories of glitches.PACS numbers: 97.60.Jd, 21.65. +f

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