Triaxial deformation, shell structure, shell corrections and the connection to alpha-clustering in nuclei

Abstract We explore the connection between the appearance of quasi-stable structures in mean-field type calculations, which arise as a result of the evolution of the underlying shell structure as a function of deformation, and α -clustering in light even–even nuclei. The Nilsson–Strutinsky mean-field approach employs a macroscopic liquid-drop whose energy is modified by a shell correction term derived using the Strutinsky method. This method reflects the variations in the energies of the single-particle states with deformation. As such, there is no obvious connection to clustering. Here we use the changing level scheme of the deformed harmonic oscillator as a function of triaxial deformation to fully explore the variation in stability of α -cluster structures in light even–even nuclei. The energies of the harmonic oscillator levels are used to deduce the energy required to disrupt the α -cluster as a function of the triaxial deformation. We find that there is good agreement between variations in the shell correction energy in the mean-field method and the energy required to disrupt the α -cluster. This provides a necessary link between understanding of the appearance of quasi-stable α -cluster structures and quasi-stable shapes appearing in mean-field calculations.