Microscopic baryon-baryon interactions at finite density and hypernuclear structure
In this work we develop a complete ab-initio framework for the calculation of microscopic baryon-baryon interactions between the lowest flavor-SU(3) octet states and their application in finite nuclei and hypernuclei. We start from the Bonn meson exchange potential model, which is extended to include also hyperons. On top of that a ... Dirac-Brueckner-Hartree-Fock formalism is developed, which can deal as well with symmetric and asymmetric nuclear matter as with hypermatter. The microscopic interactions are then applied in a low density approximation to the calculation of finite nuclei within a relativistic mean-field approximation of the density dependent relativistic hadron field theory. The work is split in two parts. In the first part we develop the formalism of a relativistic framework for ab-initio calculations of finite baryonic objects as nuclei and hypernuclei. In the the second part calculations of hypernuclear properties are presented. In chapter 1 we introduce the the formalism of relativistic scattering theory. In the discussion the relativistic integral equation for two body scattering, the Bethe-Salpeter (BS) equation is derived. After discussing the formal structure of the T-matrix, approximations to the BS equation are introduced, which are necessary to perform actual calculations. The full integral kernel is truncated to contain only the lowest order interactions and the full two baryon propagator is fixed to positive energy states and modified such in a covariant way, that retardation effects are suppressed in effective interactions. For the resulting equations the K-matrix approximation and the formalism of scattering phase shifts are explained. Chapter 2 develops then on the basis of the previous one the general formalism of meson-exchange models and its application to interactions between the members of the lowest baryon octet. This is extended in chapter 3 to the relativistic in-medium scattering theory. In this so-called Dirac-Brueckner-Hartree-Fock (DBHF) formalism, the one-body self-energies and Pauli blocking are taken into account. The structure of the Pauli operator and the self-energies are discussed in detail. In the calculation of self-energies ambiguities arise due to the neglection of negative energy states in the whole formalism. Recipes to cure this partly are discussed. The following section formulates the part of our microscopic framework to describe finite systems of baryons, the density dependent relativistic hadron field theory. The in-medium interactions obtained from DBHF calculations are mapped onto density dependent vertex functionals in DDRH theory, which account for the change of the effective interaction in the medium due to correlations. The mapping procedure and specialties arising due to the density dependent interaction are discussed. Concluding the part of the work presenting our ab-initio approach in chapter 5 we study the dynamics of baryon-baryon interactions. It is investigated how the effective interactions depend on changes in the coupling constants and masses. It is determined how well SU(3) relations are fulfilled for effective interactions as used, for example, in the standard phenomenological calculations of hypernuclei and neutron star matter. In chapter 6 a new concept for solving the BS equation in free space and at finite density is developed. The basic idea is to map the full effective interaction onto a meson exchange kernel. This amounts to a rescaling of the vertices which obtain a dependence on the Mandelstam variables and the Fermi momenta. This treatment simplifies the solution of BS equations dramatically while producing qualitatively and quantitatively similar results. In the next part of this work hypernuclear structure calculations are presented. After a short introduction to hypernuclear physics, given in chap. 7, we continue in chap. 8 with a discussion of single particle spectra of hypernuclei with large ground state spins. The first experimental indication of a spin-orbit splitting in intermediate mass hypernuclei are analyzed and discussed. In chap. 9 we present our calculations on the hypernuclear Auger effect, which provides an alternative method of spectroscopy in intermediate andheavy mass hypernuclei.