Generator Coordinate Method for Nuclear Low-Lying States: from MR-EDF to MR-IMSRG Calculations

Abstract:  Mean-field or energy density functional (EDF) methods have achieved a great success in describing many nuclear phenomena. Among the microscopic approaches to nuclear many-body problem, nuclear EDFs are the only ones that can be applied to study nuclei over the entire chart with a few universal parameters at acceptable computational costs. To go beyond the modeling of nuclear bulk properties and perform detailed calculations for nuclear excitations, one of the choices is to extend the mean-field approaches from the single-reference framework to a multi-reference one with generator coordinate method (GCM). In this framework, the dynamical correlations related to the restoration of symmetries broken in mean fields and to the fluctuations of collective degree of freedom can be taken into account efficiently. Along this direction, the so-called multi-reference energy density functional (MR-EDF) approaches have been tremendously developed by implementing the GCM into different modern EDF calculations in the recent decade. This beyond mean-field approach provides an important theoretical tool to analyze the low-energy structure of nuclei with shape coexistence and shape transition. In the mean time, with the technique of similarity renormalization group (SRG), the (multi-reference) IMSRG starting from a simple mean-field state has been developed and turned out to be successful for both close- and open-shell nuclei based on the interaction from chiral effective field theory (EFT). The above achievements inspire us to combine the virtues of GCM and IMSRG to realize an ab-initio study the low-lying states of nuclei with complex shapes. During this talk, I may show several applications of the MR-EDF method based on a relativistic energy density functional to nuclear low-lying states and the computation of nuclear matrix elements for neutrinoless double beta decay. Besides, I will show some preliminary results towards our goal of extending the MR-IMSRG approach for deformed/transitional nuclei using the chiral-EFT Hamiltonians.