Eur. Phys. J. A (2021) 57: 29
https://doi.org/10.1140/epja/s10050-020-00337-z

Regular Article – Theoretical Physics

Resonances in and : what do we learn from a microscopic cluster theory?

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

^a pdesc@ulb.ac.be

Received: 26 October 2020
Accepted: 24 December 2020
Published online: 14 January 2021

Abstract

We discuss resonance properties in three-body systems, with examples on and . We use a microscopic cluster model, where the generator coordinate is defined in the hyperspherical formalism. The nucleus is described by an structure, whereas is considered as an system. We essentially pay attention to resonances. We review various techniques which may extend variational methods to resonances. We consider and states in and . 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 ( state in ) whose radius has been calculated or measured in several works. In , we identify two resonances slightly below the three-body threshold.