https://doi.org/10.1140/epja/s10050-024-01448-7
Regular Article - Theoretical Physics
Ab initio description of monopole resonances in light- and medium-mass nuclei
IV. Angular momentum projection and rotation-vibration coupling
1
Department of Physics, Technische Universität Darmstadt, 64289, Darmstadt, Germany
2
ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291, Darmstadt, Germany
3
IRFU CEA Université Paris-Saclay, 91191, Gif-sur-Yvette, France
4
KU Leuven, Department of Physics and Astronomy, Instituut voor Kern- en Stralingsfysica, 3001, Leuven, Belgium
5
CEA, DAM, DIF, 91297, Arpajon, France
6
Laboratoire Matière en Conditions Extrêmes, Université Paris-Saclay CEA, 91680, Bruyères-le-Châtel, France
7
CEA, DES, DER, IRESNE, SPRC, 13108, Saint-Paul-lès-Durance, France
8
Helmholtz Forschungsakademie Hessen für FAIR GSI Helmholtzzentrum, 64289, Darmstadt, Germany
a
aporro@theorie.ikp.physik.tu-darmstadt.de
Received:
2
July
2024
Accepted:
3
November
2024
Published online:
27
November
2024
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 consistent 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.
© The Author(s) 2024
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