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Resonances in \(^{12}{\mathrm C}\) and \(^{24}\mathrm{Mg}\): what do we learn from a microscopic cluster theory?

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Abstract

We discuss resonance properties in three-body systems, with examples on \(^{12}{\mathrm C}\) and \(^{24}\mathrm{Mg}\). We use a microscopic cluster model, where the generator coordinate is defined in the hyperspherical formalism. The \(^{12}{\mathrm C}\) nucleus is described by an \(\alpha +\alpha +\alpha \) structure, whereas \(^{24}\mathrm{Mg}\) is considered as an \(^{16}\mathrm{O}+\alpha +\alpha \) system. We essentially pay attention to resonances. We review various techniques which may extend variational methods to resonances. We consider \(0^+\) and \(2^+\) states in \(^{12}{\mathrm C}\) and \(^{24}\mathrm{Mg}\). We show that the r.m.s. radius of a resonance is strongly sensitive to the variational basis. This has consequences for the Hoyle state (\(0^+_2\) state in \(^{12}{\mathrm C}\)) whose radius has been calculated or measured in several works. In \(^{24}\mathrm{Mg}\), we identify two \(0^+\) resonances slightly below the three-body threshold.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All numerical results in the present work can be reproduced by using the given values for the parameters.].

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Acknowledgements

This work was supported by the Fonds de la Recherche Scientifique—FNRS under Grant Numbers 4.45.10.08 and J.0049.19. It benefited from computational resources made available on the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles, infrastructure funded by the Walloon Region under the grant agreement No. 1117545.

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  1. Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles (ULB), C.P. 229, 1050, Brussels, Belgium

    P. Descouvemont

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  1. P. Descouvemont
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Correspondence to P. Descouvemont.

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Communicated by Nicolas Alamanos

Directeur de Recherches FNRS.

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Descouvemont, P. Resonances in \(^{12}{\mathrm C}\) and \(^{24}\mathrm{Mg}\): what do we learn from a microscopic cluster theory?. Eur. Phys. J. A 57, 29 (2021). https://doi.org/10.1140/epja/s10050-020-00337-z

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