Many-body Problems in the Theory of Stellar Collapse and Neutron Stars

Abstract: When modelling the collapse of massive stars leading to supernova explosions and the cooling of neutron stars, understanding the microphysical processes, such as the interaction of neutrinos within a dense medium are of vital importance. The interaction of neutrinos with nucleons (neutrons and protons) is altered by the presence of the medium, compared to the same process with free nucleons. Neutrino scattering and production processes may be characterized in terms of the excitations that are created or destroyed in the nuclear medium. One way to analyse the effects of the medium is by using Landau's theory of normal Fermi liquids. This theory gives simple relationships between physical quantities such as the spin susceptibility or the response to a weak interaction probe in terms of Landau parameters, that are measures of the interaction between quasiparticles. One problem when using Landau Fermi liquid theory for nucleon matter is that the interaction has a tensor component. The tensor interaction does not conserve the total spin and, as a consequence, there are generally contributions to long-wavelength response functions from states that have more than one quasiparticle-quasihole pair in the intermediate state. Such contributions cannot be calculated in terms of Landau parameters alone, since in the usual formulation of Landau theory, only singlepair excitations are considered. In this thesis three problems are addressed. First, we obtain bounds on the contributions from more than one quasiparticle-quasihole pair by using sum-rule arguments. Second, we derive expressions for static response functions allowing for the tensor components of the interaction. We analyse which the most important effects are on the static response of nucleon matter, and find that the major contributions comes from renormalization of coupling constants and transitions to states with more than one quasiparticle-quasihole pair. Third, we show how contributions to the dynamical response coming from states containing two quasiparticle-quasihole pairs may be evaluated in terms of Landau theory if one allows for the effect of collisions in the Landau kinetic equation. We consider the case of asymmetric nuclear matter, and our work goes beyond earlier works in that they contain the effects of collisions in addition to those of the mean field.