Resonances in 12C and 24Mg: what do we learn from a microscopic cluster theory?

We discuss resonance properties in three-body systems, with examples on C-12 and Mg-24. We use a microscopic cluster model, where the generator coordinate is defined in the hyperspherical formalism. The C-12 nucleus is described by an alpha + alpha + alpha structure, whereas Mg-24 is considered as an O-16 + 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 C-12 and Mg-24. 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 C-12) whose radius has been calculated or measured in several works. In Mg-24, we identify two 0(+) resonances slightly below the three-body threshold.

Automated summary

The study focuses on resonance properties in three-body systems, specifically looking at examples in C-12 and Mg-24 using a microscopic cluster model. Attention is paid to resonances, with a review of techniques extending variational methods to resonances. The study considers the sensitivity of the r.m.s. radius of a resonance to variational basis, particularly in relation to the Hoyle state in C-12. A total of two 0(+) resonances below the three-body threshold are identified in Mg-24.