Speaker
Description
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
