Development of Nuclear Energy Density Functionals from Optimization to Uncertainty Analysis

Abstract

This doctoral thesis covers the different aspects of the development of nuclear energy density functionals (EDFs). The nuclear EDFs are still the only microscopic models that can be applied along the whole nuclear chart. Despite their versatile applicability to predict various properties of experimentally unknown nuclei, the shortcomings of present state-of-the-art EDFs have become apparent. The deficiencies of these models must be studied, and this gained knowledge must be used to create better novel approaches. In this thesis an uncertainty analysis of the UNEDF models is carried out. Since nuclear EDFs contain a set of parameters that must be fitted to experimental data, they carry statistical uncertainty that propagates into theoretical predictions. Even though error estimates are important by themselves, the uncertainty analysis may also bring additional information as to where the deficiencies of the studied model lie. Thereby the uncertainty propagation of the UNEDF models is studied in detail in the thesis with emphasis regarding the contributions to the errors given by different model parameters. The optimization processes of nuclear EDFs are discussed by explaining different optimization strategies but also by demonstrating the difficulties of the task. Since the fitting data often includes properties of both single nuclei and infinite nuclear matter (INM), analytical formulas of INM properties are derived from a novel interaction, namely from the regularized finite-range pseudopotential.