Bose-Einstein condensation of dilute alpha clusters above the four-α threshold in ¹⁶O in the field theoretical superfluid cluster model

Observed well-developed α cluster states in 16O located above the four-α threshold are investigated from the viewpoint of Bose-Einstein condensation of α clusters by using a field-theoretical superfluid cluster model in which the order parameter is defined. The experimental energy levels are reproduced well for the first time by calculation. In particular, the observed 16.7 MeV 0+ 7 and 18.8MeV0+ 8 states with low-excitation energies from the threshold are found to be understood as a manifestation of the states of the Nambu-Goldstone zero-mode operators, associated with the spontaneous symmetry-breaking of the global phase, which is caused by the Bose-Einstein condensation of the vacuum 15.1 MeV 0+ 6 state with a dilute well-developed α cluster structure just above the threshold. This gives evidence of the existence of the Bose-Einstein condensate of α clusters in 16O. It is found that the emergence of the energy level structure with a well-developed α cluster structure above the threshold is robust, almost independently of the condensation rate of α clusters under significant condensation rate. The finding of the mechanism that causes the level structure that is similar to 12C to emerge above the four-α threshold in 16O reinforces the concept of Bose-Einstein condensation of α clusters in addition to 12C.