From cluster structures to nuclear molecules: the role of nodal structure of the single-particle wave functions

The nodal structure of the density distributions of the single-particle states occupied in rod-shaped, hyper- and megadeformed structures of non-rotating and rotating $N\sim Z$ nuclei has been investigated in detail. The single-particle states with the Nilsson quantum numbers of the $[NN0]1/2$ (with $N$ from 0 to 5) and $[N,N-1,1]\Omega$ (with $N$ from 1 to 3 and $\Omega=1/2$, 3/2) types are considered. These states are building blocks of extremely deformed shapes in the nuclei with mass numbers $A \leq 50$. Because of (near)axial symmetry and large elongation of such structures, the wave functions of the single-particle states occupied are dominated by a single basis state in cylindrical basis. This basis state defines the nodal structure of the single-particle density distribution. The nodal structure of the single-particle density distributions allows to understand in a relatively simple way the necessary conditions for $\alpha$-clusterization and the suppression of the $\alpha$-clusterization with the increase of mass number. It also explains in a natural way the coexistence of ellipsoidal mean-field type structures and nuclear molecules at similar excitation energies and the features of particle-hole excitations connecting these two types of the structures. Our analysis of the nodal structure of the single-particle density distributions does not support the existence of quantum liquid phase for the deformations and nuclei under study.