Antisymmetrized four-body wave function and coexistence of single particle and cluster structures

It is shown that each Yakubovski component of the totally antisymmetric four-body wave function satisfies the same equation as the unantisymmetric wave function. In the antisymmetric total wave function, the wave functions belonging to the same kind of partition are totally antisymmetric among themselves. This leads to the coexistence of cluster models, including the single particle model as a special case of the cluster model, as a sum. NUCLEAR STRUCTURE Four-body problem. Antisymmetrization. Decoupled Yakubovski equation. Cluster models. Coexistence with single particle model.