The 12C nucleus as a 3α system with forbidden states

We have calculated the 0₁⁺ ground state and the 0₂⁺ and 0₃⁺ first excited states of ¹²C in the model of three α-particles whose interaction is described using a local attractive potential with forbidden states, which well reproduces the α-α scattering phases. The methods of projection of the states forbidden by the Pauli exclusion principle in a system of three composite particles are discussed. The results of the calculation show that the condition of orthogonality to the forbidden states is sufficient to prevent the system from collapse. The binding energy value obtained (15.06 MeV) is somewhat overestimated. This discrepancy seems to come from neglecting triple exchanges of nucleons of different α-particles and from the fact that the ¹²C real nucleus differs from the 3α system.