Improvement of nuclear interaction parameters for relativistic mean field model

Calculations of nuclear properties of nuclei such as binding energies, single particle levels, electric moments, charge radii and nucleon radii are possible by using mean field approach on the wide region covers stable nuclei, neutron rich and proton rich nuclei. The Relativistic Mean Field (RMF) model based on quantum hydrodynamics is a successful model because of its success in describing nuclear interaction originating from its phenomenology and its ability to be used in nuclear density matter investigations. This model is based on the assumption that the nucleons interact each other via exchange of various mesons. Because of that, the terms for meson masses, meson-nucleon coupling constants and self-coupling of some mesons in this model can be determined by using experimental data of a small numbers of nuclei and later nuclear properties of nuclei can be calculated by using this model. This requires well defined a set of parameters consisting of meson masses and interaction constants. In this thesis, an investigation has been made on how the parameter set for the non-linear RMF model can be improved instead of standard fitting by using Artificial Neural Networks (ANN) successfully used in determining non-linear relations. In this framework, a new RMF model parameter set called DEFNE has been developed and its success has been tested in a wide region covers the periodic table. This study has revealed that the ANN method can determine the non-linear relationship between the values of the RMF model parameter sets and the values of the various nuclear properties obtained by using them in the RMF model. Following this result, the parameter set called DEFNE for the RMF model was developed. This set of parameters has been used in the RMF model to calculate the ground state binding energies and charge radii of about 140 nuclei selected from the light to heavy nuclei in the periodic table. The calculated results for ground state binding energies have been compared with the results of RMF model with NL3* parameter set, Hartree-Fock-Bogoliubov method (SKP and SLy4 parameter sets) and the liquid drop model. As a result of this study, it has been determined that the newly developed DEFNE parameter set is effective in the successful prediction of nuclear binding energies and charge radii in a wide range of nuclei region covers the periodic table. However, when the nuclear matter properties of the parameter set are investigated, it can be concluded that it cannot be very effective in determining the surface properties of nuclei. This is due to the self-interaction terms of the sigma meson, and it is suggested that the self-interaction parameters of the meson-nucleon and mesons can be considered independently of each other in the process of developing the parameter set for RMF model.