The Low-Energy Quadrupole Mode of Nuclei

TL;DR

This paper reviews various theoretical models and methods for understanding low-energy quadrupole excitations in nuclei, emphasizing triaxiality signatures and recent advances in microscopic and phenomenological approaches.

Contribution

It provides a comprehensive comparison of phenomenological and microscopic models, including recent developments like the Generator Coordinate Method and mean field mapping techniques.

Findings

Microscopic models successfully reproduce quadrupole spectra.

Generator Coordinate Method offers insights into triaxial nuclei.

Mean field mapping improves phenomenological parameter determination.

Abstract

The phenomenological classification of collective quadrupole excitations by means of the Bohr Hamiltonian is reviewed with focus on signatures for triaxility. The variants of the microscopic Bohr Hamiltonian derived by means of the Adiabatic Time Dependent Mean Field theory from the Pairing plus Quadrupole-Quadrupole interaction, the Shell Correction Method, the Skyrme Energy Density Functional, the Relativistic Mean Field Theory, and the Gogny interaction are discussed and applications to concrete nuclides reviewed. The Generator Coordinate Method for the five dimensional quadrupole deformation space and first applications to triaxial nuclei are presented. The phenomenological classification in the framework of the Interacting Boson Model is discussed with a critical view on the boson number counting rule. The recent success in calculating the model parameters by mapping the mean field deformation energy surface on the bosonic one is discussed and the applications listed. A critical assessment of the models is given with focus on the limitations due to the adiabatic approximation. The Tidal Wave approach and the Triaxial Projected Shell Model are presented as practical approaches to calculate spectral properties outside the adiabatic region.