Probing nuclear cluster symmetries through the harmonic oscillator

The present contribution explores the symmetries of the deformed harmonic oscillator for both prolate and oblate deformations. It demonstrates the emergence of clustering from the degeneracies of the deformed harmonic oscillator and the appearance of the cluster structures in the associated densities. The universality of molecular structures is presented, demonstrating that molecular-like exchange of protons and neutrons is encoded into the mean-field. The nature of oblate-like structures is also explored.