Correlations in nuclear matter at low densities in an extended relativistic mean-field model.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2013)
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|Item Type:||Ph.D. Thesis|
|Title:||Correlations in nuclear matter at low densities in an extended relativistic mean-field model|
Knowledge of the equation of state of strongly interacting matter is required for the description of the variety of nuclear matter phases in a wide range of densities, temperatures, and proton fractions. A specifically important problem is the construction of equations of state for astrophysical applications, e.g for the investigation of various stages of core-collapse supernova explosions and the structure of proto-neutron and neutron stars.
For many years, a very small number of equation of state tables was available that have been used in simulations of dynamical astrophysical processes covering the full parameter space needed. These equations of state often do not supply sufficient information on the thermodynamic and compositional details and do not take into account all relevant phase transitions when multiple phases co-exist. In recent years, the appearance of new experimental data on atomic nuclei,heavy-ion-collisions and from astrophysical observations as well as the progress in the theoretical description of the nuclear matter properties and significant improvements of supercomputers have triggered new developments for constructing equations of state. Nevertheless, existing microscopic approaches still do not allow to construct a description in the whole range of densities and temperatures. Thus, approximations and simplifications are needed to develop practical schemes. Thereby, different phenomenological approaches to the equation of state continue to be developed.
In this work we study the effect of two specific types of correlations on thermodynamic properties of nuclear matter within the framework of a generalized relativistic mean-field model with light clusters as additional degrees of freedom beyond nucleons. In particular, these correlations include two-body scattering contributions and pairing effects. They appear due to the short-range nucleon-nucleon interaction at low densities and modify the composition and thermodynamic properties of matter. These effects should be included in the equation of state since in this density regime they may strongly influence the structure of the proto-neutron star, the effectiveness of the neutrino re-heating of the shock wave in supernova simulations and the cooling history of neutron stars.
This thesis is divided into two major parts. In the first major part we introduce a generalized relativistic mean-field model that includes clusters and two-nucleon scattering correlations in an effective way as explicit degrees of freedom in the thermodynamic potential. These bound and scattering states are represented by quasiparticles with density and temperature dependent properties. All relevant quantities are derived in a thermodynamically consistent way. The model reproduces relativistic mean field results around nuclear saturation density, where clusters are dissolved. The low-density behavior of nuclear matter at finite temperatures with nucleons and light nuclei is considered within a fugacity expansion of the grand canonical potential by comparing the virial equation of state with the generalized relativistic mean field approach. From the comparison of the expansions consistency relations are derived, which connect quasiparticle parameters with the meson-nucleon couplings of the relativistic mean-field model in the vacuum and the phase shifts or effective-range parameters of nucleon-nucleon scattering.
The second major part of this thesis is devoted to the investigation of the effect of pairing correlations on the thermodynamic properties of pure neutron matter for densities up to saturation. Here we extend the relativistic mean field model by including pairing correlations in the 1S0 nn channel. Calculations are performed with a Yamaguchi separable potential. Pairing gaps are computed for various temperatures. The results for thermodynamic quantities are compared with relativistic Fermi gas calculations. An overall variation in the pressure of 10 % is observed for a given model due to pairing.
|Place of Publication:||Darmstadt|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 530 Physik|
|Divisions:||05 Department of Physics
05 Department of Physics > Institute of Nuclear Physics
|Date Deposited:||28 Mar 2013 10:35|
|Last Modified:||28 Mar 2013 10:35|
|Referees:||Langanke, Prof. Dr. Karlheinz and Roth, Prof. Dr. Robert|
|Refereed:||21 December 2012|