Ab initio description of monopole resonances in light- and medium-mass nuclei: IV. Angular momentum projection and rotation-vibration coupling

TL;DR

This paper develops a consistent approach to treat vibrational and rotational excitations in nuclei by emphasizing the importance of angular momentum restoration in ab initio calculations, specifically for giant monopole resonances.

Contribution

It introduces a method that incorporates angular momentum projection within the PGCM framework to accurately describe collective nuclear motions.

Findings

Angular momentum restoration prevents unphysical coupling in monopole responses.

Performing angular momentum projection after solving the secular equation causes contamination.

A priori angular momentum restoration is essential for consistent treatment of vibrations and rotations.

Abstract

Giant Resonances are, with nuclear rotations, the most evident expression of collectivity in finite nuclei. These two categories of excitations, however, are traditionally described within different formal schemes, such that vibrational and rotational degrees of freedom are separately treated and coupling effects between those are often neglected. The present work puts forward an approach aiming at a consitent treatment of vibrations and rotations. Specifically, this paper is the last in a series of four dedicated to the investigation of the giant monopole resonance in doubly open-shell nuclei via the ab initio Projected Generator Coordinate Method (PGCM). The present focus is on the treatment and impact of angular momentum restoration within such calculations. The PGCM being based on the use of deformed mean-field states, the angular-momentum restoration is performed when solving the secular equation to extract vibrational excitations. In this context, it is shown that performing the angular momentum restoration only after solving the secular equation contaminates the monopole response with an unphysical coupling to the rotational motion, as was also shown recently for (quasi-particle) random phase approximation calculations based on a deformed reference state. Eventually, the present work based on the PGCM confirms that an a priori angular momentum restoration is necessary to handle consistently both collective motions at the same time. This further pleads in favor of implementing the full-fledged projected (quasi-particle) random phase approximation in the future.