Clustering effects in a microscopic four-α description of the α+12C system

The α${+}^{12}$C system is investigated in the generator coordinate method, where the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ nucleus is described by three α particles located on the apexes of an equilateral triangle. The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ wave functions are projected out on the $0^{+}$ and $2^{+}$ states. By modifying the size of the triangle, we analyze the importance of clustering effects in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ on ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ bound states, and on α${+}^{12}$C phase shifts. These effects are found to be reduced when the total spin of the α${+}^{12}$C system increases. The coupling between the α${+}^{12}$C($0^{+}$) and α${+}^{12}$C($2^{+}$) channels also decreases when α clustering is introduced in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. We obtain high-energy resonances in the α${+}^{12}$C scattering. These resonances, located between 15 and 30 MeV in the center of mass, are suggested to be Pauli resonances, analog to the well-known forbidden states in the two-cluster model.