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Dense nuclear matter

The discovery of neutron stars (NS's) in the form of pulsars has been a major stimulus to studies of dense matter. According to our present understanding, neutron stars have a rich structure. The outermost layers are rather similar to terrestrial crystalline matter. With increasing depth in the star, and thus increasing density, nuclei become more neutron-rich until at a density of about one thousandth of nuclear nuclear density, nuclei reach the neutron drip line. At higher densities nuclei coexist with a neutron liquid, and they eventually dissolve just below nuclear density. Key questions concern the equation of state of matter as a function of density, temperature, the total proton/nucleon ratio Ye, the weak interaction rates shifting Ye to its equilibrium value, and neutrino emission processes. The quest to understand the interiors of these objects, which are much denser and more neutron-rich than laboratory nuclei, led to the development of many-body techniques able to treat strong correlations. An important achievement of the past two decades is that there is now a remarkably good agreement among the various microscopic calculations of the properties of dense neutron matter up to about nuclear matter density. The results are essentially independent of the many-body technique and the two-body nucleon-nucleon interaction, provided the latter fits nucleon-nucleon scattering data. Close to nuclear matter density, nuclei may be rod-like or plate-like. This was first realised in the context of stellar collapse, but has now been shown to be important also for neutron stars. These phases are potentially very important for understanding a number of aspects of neutron star behaviour, especially the sudden jumps in the rotational frequencies observed in a number of pulsars [37]. To understand nuclear phenomena in neutron-rich matter one needs more reliable effective interactions. Microscopic many-body calculations of finite systems can be used to improve models of effective interactions. At the present time it is possible, with the Green's function Monte-Carlo method, to make essentially exact calculations of the energy of nuclei up to A=7 and for systems of up to 8 neutrons. For larger systems, good estimates of properties can be obtained using the cluster variational Monte Carlo method. These methods are now beginning to yield important contributions. In particular, for pure neutron systems the spin-orbit interaction is found to be suppressed by about a factor of two in comparison to symmetric nuclear matter. Matter at densities above nuclear density occurs both in the interiors of cold neutron stars as well as in stellar collapse (e.g. supernovae) or neutron star mergers. In the laboratory, collisions between heavy ions are the only direct way of studying the properties of dense matter. In this case matter is roughly isospin symmetric, and has zero strangeness. The situation is different in neutron stars, because the lifetime is very large compared with weak interaction times, i.e. Ye is much less than that in laboratory nuclei. At high densities matter consists of interacting baryons (neutrons, protons, and possibly hyperons and other particles) and/or quarks in beta-equilibrium with leptons. In addition, Bose condensates of pions or kaons may be present. The key problems are to understand the interactions between possible constituents and develop reliable techniques for calculating the properties of a strongly-correlated, relativistic system of hadrons [38]. This is crucial, because 95% of the matter in a neutron star is located in regions with supranuclear densities, where different equations of state "on the market" can vary strongly and lead to maximum neutron star masses ranging from 1.4 to roughly 2.8 M$_\odot$. There exists a growing group of milisecond pulsars (rotating neutron stars with periods below 10 ms). The finding of rotation periods less than 1 ms would challenge present models. Another crucial area is that of neutrino processes in neutron stars and in matter in a collapsing star. Emission of neutrinos is the dominant mechanism for loss of heat from a neutron star during the first 105 -106 years of its life, and the measurement of the surface temperatures of neutron stars provides a way of probing neutrino processes in the star. Since neutrino emission rates are very sensitive to the constituents of dense matter, such measurements are a promising way of gleaning information about the deep interiors of neutron stars. In addition to the neutrino emission, absorption and scattering processes discussed in 2.3 and 3.7, the effects of correlations in matter needs to be further explored. 
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