Variational studies of nucleon matter with realistic potentials

We study cold, symmetric nuclear matter and pure neutron matter at densities up to six times nuclear saturation density, with realistic interactions fitted to nucleon-nucleon scattering data, using variational methods and correlated wave functions. The expectation value of the nuclear Hamiltonian is expanded in terms of cluster contributions, and re-summed via chain summation methods. Included in the calculation are a number of new, momentum-dependent cluster diagrams, which make significant contributions to the energy. These include relativistic boost corrections, heretofore neglected in studies of infinite matter. The boost corrections, partially mocked up by the three-nucleon interaction in previous studies, must be treated explicitly to obtain accurate predictions of the energy of matter at densities above saturation. We find that matter exhibits structure on the femtometer scale at saturation density, and undergoes a phase transition at about twice saturation density. The new phase is marked by a significant increase in the length of tensor correlations. The nature of the transition is further elucidated using the spin-isospin structure function, which points to long-range order in the new phase. We argue that this new phase contains a neutral pion condensate, as evidenced by enhancement of the pionic interactions and the pion field. In addition to symmetric nuclear and pure neutron matter, we present an equation of state for beta-stable matter, used to predict properties of spherical, non-rotating neutron stars by integrating the relativistic equation governing gravitational equilibrium. The interaction models presented here, with relativistic boost corrections, predict the existence of neutron stars with masses up to 2.0 to 2.2 solar masses. We also investigate the possibility of a deconfined quark phase in neuron star cores, and argue that such a phase, should it be present, will have only a small effect on the predictions of maximum masses.