Nuclear physics and dense matter

Abstract

Crucial to understanding the properties of dense matter in supernova explosions and neutron stars is determining the role of the nuclei present in such matter. Because many of the properties of the matter do not depend strongly on the fine details of nuclear structure, the liquid drop model of the nucleus provides a convenient starting point. The influence of the matter outside the nuclei on the properties of the nuclei must, however, be taken into account. In this thesis we study several aspects of the liquid drop model and its applications. In particular we first study the theory of surface tension as used in the liquid drop model. We then develop a refined version of the compressible liquid drop model, which enables us to redetermine semi-empirically the properties of bulk nuclear matter. Finally, we apply the resultant nuclear mass formula to the equation of state of hot, dense matter. In part A we examine the concept of surface tension and study the consequences of relaxing the assumption that the surface tension of all nuclei is isotropic. First we present a macroscopic theory of anisotropic surface tension. Then, with a particular choice for the functional form of the surface tension tensor, we apply this theory in the case of a uniformly charged liquid drop. We show that a small anisotropy in the surface tension can significantly distort a highly charged drop and lower its fission barrier without greatly affecting the total energy. The theory developed in part A shows how the concept of surface tension enters the liquid drop model. This knowledge is applied in part B where we develop a refined version of the compressible liquid drop model introduced by Baym, Bethe and Pethick. By fitting this model to the binding and Coulomb energies of heavy nuclei, we redetermine phenomenologically the bulk and surface properties of symmetric nuclear matter. The principal refinement made is in the description of the surface tension, the semi-phenomenological expression used here being constructed to agree with microscopic surface energy calculations. The resulting six parameter mass formula reproduces known nuclear masses with an rms deviation of 2 2.6 MeV/c (attributable primarily to shell effects). Because the compressible liquid drop model contains the physics needed to describe both ordinary and neutron star nuclei, we expect this mass formula to be a reliable indicator of highly neutron-rich nuclei. The compressible liquid drop mass formula is used in part C where we present a simple calculation of the equation of state of hot, dense matter for application to hydrodynamic calculations of the collapse of massive, highly evolved stars. The temperatures and densities we consider range from 5 x 10^9 to 5 x lO^ll K and 109 to 1014 g/cm3, with the low temperature, high density region excluded. Heavy nuclei are represented by a single, characteristic species whose neutron and proton numbers are determined thermodynamically. The binding energies of these nuclei are determined from the mass formula described in part B. We treat all particles present in the. matter as perfect gases but include ion-ion Coulomb correlation effects with a simple Wigner-Seitz correction.U of I OnlyThesi