Microscopic effective interactions in neutron -rich matter

We present a study of effective interactions in the nuclear medium, with particular emphasis on dense and neutron-rich matter. The properties of in-medium effective interactions are reflected in what is known as the nuclear equation of state, defined as the energy per particle as a function of density (and other degrees of freedom, when appropriate). The conditions under which our predictions can be tested are produced in the laboratory via energetic heavy-ion collisions or can be found in astrophysical systems.;Our approach is microscopic in that we start from the free-space nucleon-nucleon force and proceed to calculate in-medium interactions without phenomenological adjustment of parameters. In particular, we apply realistic meson-exchange nucleon-nucleon potentials and operate within the Dirac-Brueckner-Hartree-Fock framework, which treats the motion of nucleons in the medium relativistically.;Within this framework we calculate in-medium nucleon-nucleon scattering cross sections and examine their sensitivity to the presence of asymmetry between neutron and proton densities. We find that the effect of asymmetry can be significant in specific regions of the phase space under consideration. The role of Pauli blocking of the final scattering states is investigated. Our predictions can be useful for potential applications in heavy-ion collision transport calculations.;In the second part of this work, we concentrate on astrophysical applications of the equation of state. We calculate gravitational masses and radii of non-rotating (static) neutron stars for two cases: (1) pure neutron matter, and (2) nuclear matter in generalized beta-equilibrium. Our results are compared with other theoretical predictions and recent observational data. Suggestions for further study are discussed.;Finally, we present a microscopic calculation of the properties of spin polarized neutron matter. The focal point is the effect of a net spin polarization on the equation of state. The possibility of a phase transition to a totally polarized state is investigated and discussed.