0+ states of the 12C nucleus:: the Faddeev calculation in configuration space

The Faddeev equations in configuration space are used to study the C-12 nucleus considered as the 3 alpha 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 C-12 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 alpha d cluster inside the C-12 nucleus. The calculations of the energies of several low-lying levels of C-12 reveal unnaturally large contributions from the higher partial waves of the alpha alpha 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.