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

Abstract

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

Clusters in light nuclei: history and recent developments

“…[309]. The impact of the variational basis used to describe resonances in three-body systems in the context of the alpha cluster mode of the nucleus is critically reviewed in [310], with applications to the energy position and radii of 12 C and 24 Mg states.…”