0⁺states of the¹²C nucleus: the Faddeev calculation in configuration space

Abstract

The Faddeev equations in configuration space are used to study the 12C nucleus considered as the 3α cluster system. The model includes a phenomenological (Ali–Bodmer) pair potential having s, d and g partial wave components, a three-body potential and takes into account the Coulomb interaction. The range parameter of the three-body potential is fixed by adjusting the position of the diffraction minimum of the 12C elastic form factor. To choose this parameter, we apply an s-wave model that allows us to reproduce well observed characteristics of the 0+1 and 0+2 states. The model must be supplemented by the assumption of a distortion in the charge density of an α cluster inside the 12C nucleus. The calculations of the energies of several low-lying levels of 12C reveal unnaturally large contributions from the higher partial waves of the αα potential. We did not find the additional broad 0+ resonance which was recently reported (Kurokawa C and Kato K 2005 Phys. Rev. C 76 021301-1). The calculated resonance energies for the 0+3 and 0+4 states are in satisfactory agreement with the experimental data.

Consistent α-cluster description of the 12C(0 2 + ) “hoyle” resonance

“…Next, the assumption on the "frozen" nucleon distribution in the α-particles is used to calculate the experimentally observable nucleonic structural characteristics, e. g., the root-mean-square (r. m. s.) radii and the transition radius R 12 . This extended α-cluster model leads generally to a satisfactory description of the 12 C nucleus [10,[13][14][15]20]. In particular, the calculated Γ and M 12 [13,14] are in reasonable agreement with experimental data (up to a factor two) even for the simplified local α -α interactions.…”

Microscopic cluster description of12C

“…This was e.g. done within so-called semimicroscopic models (considering structureless α-particles) [2,3,4,5,6,7,8] and within fully microscopic models [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24].…”

Continuum resonances with shielded Coulomb-like potential and Efimov effect

“…Obviously, a more detailed calculation should still be made in order to verify the extension of our results, as the two-body potential used in this toy model is not including higher partial waves, which are crucial to describe correctly the properties of 12 C [15][16][17]. A detailed analysis of the structure of the Hoyle state in 12 C, based on precise electron scattering data, can be found in [27].…”

“…We should mention here that the two-body potential used in this toy model does not consider higher partial waves, in particular d and g waves, which give a significant contribution to the properties of 12 C [15]. Much more realistic calculations can be found in [16,17].…”