Cluster models from RGM to alpha condensation and beyond

Abstract

The purpose of this article is firstly to review the study of the cluster-gas-like structure, especially the α-cluster-condensate-like structure, which is a novel type of nuclear structure. The second purpose is to explain the recent proposal of the container model of general cluster dynamics which is a novel powerful cluster model that may be adopted in place of the traditional cluster models of resonating group method (RGM) and generator coordinate method (GCM) of Brink wave functions. The container model has been proposed based on the Tohsaki–Horiuchi–Schuck–Röpke (THSR) wave function which was introduced to investigate the α-cluster-condensate-like states. The main reason for the introduction of the container model was the striking fact that the RGM/GCM wave functions of various cluster states which include both gas-like and non-gas-like states are almost 100% equivalent to single THSR wave functions. For the sake of historical evolution, we give a concise review of various cluster models before the introduction of the THSR wave function. In particular, because the idea of the cluster-gas-like structure was proposed in the 1970s for explaining the properties of the Hoyle state, this review of traditional cluster models is indispensable. In view of the importance of the THSR wave function, various characteristic properties of the THSR wave function are explained. Since, at least until now, most calculations of matrix elements with the THSR wave functions have been done only analytically in order to get sufficient numerical accuracy, some analytical manipulations of the THSR wave function will be explained.