Cluster formations in deformed states for ${}^{28}$Si and ${}^{32}$S

We study cluster formation in strongly deformed states for ${}^{28}$Si and ${}^{32}$S using a macroscopic-microscopic model. The study is based on calculated total-energy surfaces, which are the sums of deformation-dependent macroscopic-microscopic potential-energy surfaces and rotational-energy contributions. We analyze the angular-momentum-dependent total-energy surfaces and identify the normal- and super-deformed states in ${}^{28}$Si and ${}^{32}$S, respectively. We show that at sufficiently high angular momenta strongly deformed minima appear. The corresponding microscopic density distributions show cluster structure that closely resemble the ${}^{16}$O+${}^{12}$C and ${}^{16}$O+${}^{16}$O configurations. At still higher deformations, beyond the minima, valleys develop in the calculated surfaces. These valleys lead to mass divisions that correspond to the target-projectile configurations for which molecular resonance states have been observed. We discuss the relation between the one-body deformed minima and the two-body molecular-resonance states.