Uncertainty analysis and symmetry restoration in nuclear self-consistent methods

Abstract

This thesis contains two articles, in the following denoted by I and II, and an introduction to them. In Chapter 1, I present the theoretical models of nuclear structure. In Chapter 2, I introduce the basic ideas about the density functional theory (DFT) and self-consistent mean-field (SCMF) calculations. In Chapter 3, I give the formulae for the uncertainty propagation, which is the error analysis method used in article I. As a proper tool to survey the predictive power of theoretical models, the error analysis now has become more and more widely used. By analyzing the propagation of uncertainties, one tries to find out the e ectiveness of the calculation with a given parameter set obtained from optimization. In Chapter 4, I present the theoretical framework of the Lipkin method used in article II. This method can be considered as an approximation of the variation-after-projection method. In Chapter 6, I brie y review the main results of articles I and II. In the Appendices, I give some useful details and derivations.