Inclusion of the spin-orbit force in an α-cluster model

A simplified treatment is proposed to take into account the effect of the spin-orbit force within the framework of the conventional α-cluster model for light nuclei. It is very important for a study of the stability of α-cluster structure in light nuclei to include the effect of the spin-orbit force, but it has been considered that its inclusion is not so easy because (0s)⁴ internal states are usually assumed for α-clusters in the model. The proposed method introduces states with 44…431] spatial symmetry by means of an operator which is just equal to a one-body spin-orbit potential. The method is applied to a 3α cluster model for ¹²C.