Microscopic derivation of the Bohr-Mottelson collective Hamiltonian and its application to quadrupole shape dynamics

TL;DR

This paper microscopically derives the Bohr-Mottelson collective Hamiltonian for quadrupole shape dynamics, enabling detailed modeling of large-amplitude nuclear shape changes and coexistence phenomena.

Contribution

It provides a microscopic derivation of the five-dimensional collective Hamiltonian including shape fluctuations and rotations, advancing the theoretical understanding of nuclear quadrupole dynamics.

Findings

Derivation of the collective Hamiltonian from microscopic principles.

The five-dimensional Schrödinger equation describes shape coexistence.

The approach captures large-amplitude quadrupole shape dynamics.

Abstract

We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian of Bohr and Mottelson, which describes low-frequency quadrupole dynamics. 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 summarize the modern concepts of microscopic theory of large-amplitude collective motion, which is underlying the microscopic derivation of the Bohr-Mottelson collective Hamiltonian.