Progress and perspective on the study of the BEC-analog structure in nuclei

The second 0+ excited state at 7.65 MeV in 12C, known as the Hoyle state, is located near the 3-𝛼 breakup threshold and possesses a typical BEC-analog structure. This observation has triggered the intensive theoretical studies of the condensation configuration in nuclear systems, typically represented by the THSR wave function. In the mean time, the experimental investigation of the Hoyle-like states in heavier nuclei has been advanced quite slowly, due mostly to the difficulties in detecting multi-fragments in coincidence and the clarification of the reaction-decay mechanisms. We give here a review of the theoretical and experimental progresses in this field by taking into account the latest experimental outcomes for the 4-𝛼 resonances in 16O. Some perspectives are also given towards the possible BEC-like states in neutron-rich systems, which would be of particular importance in exploring the properties of the heavier neutron-rich nuclei and also the neutron stars.