0+ states of the 12C 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.