Supersolidity of ? cluster structure in 40Ca

alpha cluster structure in nuclei has been long understood based on the geometrical configuration picture. By using the spatially localized Brink alpha cluster model in the generator coordinate method, it is shown that the alpha cluster structure has the apparently opposing duality of crystallinity and condensation, a property of supersolids. To study the condensation aspects of the alpha cluster structure a field theoretical superfluid cluster model (SCM) is introduced, in which the order parameter of condensation is incorporated by treating rigorously the NambuGoldstone mode due to spontaneous symmetry breaking of the global phase. The alpha cluster structure of 40Ca, which has been understood in the crystallinity picture, is studied by the SCM with ten alpha clusters. It is found that the alpha cluster structure of 40Ca is reproduced by the SCM in addition to 12C reported in a previous paper, which gives support to the duality of the alpha cluster structure. The emergence of the mysterious 0+ state at the lowest excitation energy near the alpha threshold energy is understood to be a manifestation of the Nambu-Goldstone zero mode, a soft mode, due to the condensation aspect of the duality similar to the Hoyle state in 12C. The duality of alpha cluster structure with incompatible crystallinity and coherent wave nature due to condensation is the consequence of the Pauli principle, which causes clustering.

Automated summary

This study analyzes the dual nature of crystallinity and condensation in the alpha cluster structure in nuclei and finds that it is a property of supersolids. By introducing a superfluid cluster model, the alpha cluster structure of 40Ca is studied and reproduced, supporting the dual nature of the alpha cluster structure.