Advances on clusters and correlations in nuclear structure and reactions

Recent advances obtained in the last few years by the Theoretical Nuclear Physics group in Padova with various collaborators on alpha-cluster models and on nuclear correlations in stable and unstable light nuclei are reviewed in this contribution. The algebraic cluster model assumes triangular and tetrahedral arrangement of α particles for ¹²C and ¹⁶O respectively. The description of the low-lying states achieved in this model, that is a consequence of the requirement of discrete symmetries, is extremely good. We have made several calculations of α-transfer form factors and reaction cross-sections obtaining a good agreement with available data, thus corroborating the main hypotheses of the model [1]. We have speculated about smoking-gun nuclear fluorescence experiment that might shed light on the exact spatial arrangement of alpha particles in ¹²C [2]. We will also talk about the successful predictions on the positioning of ²⁹F on the southern shore of the island of inversion [3] and on recent calculations on its halo character and dipole response [4, 5]. Extension of these calculations to ³¹F [6], pointing out the presence of a halo, are also discussed.