Microscopic derivation of the quadrupole collective Hamiltonian for shape coexistence/mixing dynamics

TL;DR

This paper derives a microscopic five-dimensional quadrupole collective Hamiltonian from mean-field theory to describe complex shape coexistence and mixing phenomena in atomic nuclei.

Contribution

It provides a new derivation of the collective Hamiltonian for quadrupole modes, linking time-dependent mean-field approaches with shape dynamics.

Findings

The derived Hamiltonian successfully describes large-amplitude shape coexistence.

The approach connects time-dependent mean-field theory with collective shape phenomena.

It offers a framework for understanding quadrupole shape mixing in nuclei.

Abstract

Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinate and collective momentum, we microscopically derive the collective Hamiltonian for low-frequency quadrupole modes of excitation. We show that the five-dimensional collective Schr\"odinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We focus on basic ideas and recent advances of the approaches based on the time-dependent mean-field theory, but relations to other time-independent approaches are also briefly discussed.