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May 13 – 17, 2019
Venice, Centro Culturale Don Orione Artigianelli
Europe/Rome timezone
NSD2019 Proceedings are now available online at

Three-body description of ¹²C: From the hyperspherical formulation to the algebraic cluster model and its application to alpha+¹²C inelastic scattering

Not scheduled
SALA PALLADIO (Centro Culturale Don Orione Artigianelli)


Centro Culturale Don Orione Artigianelli


Dr Jesus Casal (PD)


Alpha clustering in ¹²C , as well as the nature of the Hoyle state (which plays a fundamental role in nucleosynthesis), have become long-standing issues. Microscopic theories [1] sustain three-alpha cluster configurations for the ¹²C nucleus, a fact which supports the use of cluster [2] and algebraic [3] methods. These approaches, although simpler, are particularly suitable for the description of reaction observables.

First, we have studied the structure of ¹²C by solving the problem of three identical S=0 bosons within the hyperspherical formalism. For this purpose, we have employed the pseudostate method in a transformed harmonic oscillator basis [4]. In this scheme, we compute radii and electromagnetic transition amplitudes. By studying the spatial distribution of the system in terms of Jacobi coordinates, we find equilateral triangle configurations for the 0⁺,2⁺ bound states. In the case of the 0⁺ Hoyle state, the probability exhibits a complex structure (already reported in [2,5]). However, the mean value is also consistent with the equilateral ratio, indicating that the triangular symmetry is still valid. This gives a robust basis to algebraic models of three alpha particles.

We then construct densities and transition densities in ¹²C by using the algebraic picture by Iachello and Bijker [3,6]. The ground-state band is associated with the fully symmetric representation of $D_{3h}$ with zero quanta of excitation, while the Hoyle band is characterized as a vibrational "breathing mode". The different size associated to the g.s. and Hoyle bands, as well as the reported transition amplitudes, can be described by fixing a small set of parameters. From these transition densities, we compute form-factors for the alpha+¹²C scattering following a double-folding procedure. Coupled-channel calculations using these ingredients are in progress.

1) PRL98(2007)032501
2) PRC87(2013)054615
3) NPA966(2017)158
4) PRC94(2016)054622
5) PRC90(2014)061604
6) PRL112(2014)152501

Primary authors

Dr Jesus Casal (PD) Prof. Lorenzo Fortunato (PD) Dr Giuseppe Edoardo Lanza (CT) Prof. Andrea Vitturi (PD)

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