Comparison of multi-ℎω shell-model results with MCAS

A multi-channel algebraic scattering (MCAS) method has been used to obtain spectra of a number of light-mass nuclei, which are treated as a two-cluster system, here specifically a nucleon plus a nucleus. To date, collective models have been used to specify the interactions between the nucleon and the low-lying states of the nucleus that form the compound. For the case of the carbon isotopes, these studies have been complemented by sufficiently complex and complete shell-model calculations. Comparisons with the multi-ℎω shell-model results provide new insights into the validity of those from MCAS. Our shell-model results show that the proton core in the Carbon isotopes is not passive. All shell-model states have components with 1 or 2 protons in the 0p_1/2 sub-shell so that those proton aspects can contribute significantly to the 2⁺ excitation of the core of ¹⁴C