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
Received:
26
October
2020
Accepted:
24
December
2020
Published online:
14
January
2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
