Microscopic three-cluster study of light exotic nuclei

Abstract

I develop a microscopic three-cluster model for exotic light nuclei. I use the hyperspherical formalism, associated with the Generator Coordinate Method. This model is well adapted to halo nuclei, since the long-range part of the radial wave functions is accurately reproduced. The core wave functions are described in the shell model, including excited states. This technique provides large bases, expressed in terms of projected Slater determinants. Matrix elements involve sevendimension integrals, and therefore require long calculation times. I apply the model to 11 Li, 14 Be, 15 B, and 17 N described by two neutrons surrounding a 9 Li, 12 Be, 13 B and 15 N core, respectively. The 17 Ne (as 15 O+p+p) and 15 Ne (as 13 O+p+p) mirror nuclei are briefly discussed. I present the spectra and some spectroscopic properties, such as r.m.s. radii or E2 transition probabilities. I also analyze the importance of core excitations.

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

“…For the sake of clarity, we limit the presentation to clusters with spin 0 (a generalization can be found in Ref. [24]). The total wave function of the system is written as…”

“…In the present paper, we focus on two α nuclei: 12 C and 24 Mg, which are described by three-body structures (3α and 16 O + α + α, respectively). Over the last 20 years, there was a strong interest on 12 C, and in particular on the 0 + 2 resonance, known as the Hoyle state [14].…”

“…With 12 C and 24 Mg as typical examples, we discuss more specifically the determination of resonance properties in cluster models. As resonances are unbound, a rigorous treatment would require a scattering model, with scattering boundary conditions.…”

“…Section 3 is devoted to a brief discussion of different techniques dealing with resonances. The 12 C and 24 Mg nuclei are presented in Sects. 4 and 5, respectively.…”

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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.

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