Container evolution for cluster structures in $^{16}{\rm O}$

Abstract

Background: $\alpha+{^{12}{\rm C}}$ clustering in $^{16}{\rm O}$ has been of historical importance in nuclear clustering. In the last 15 years the $4\alpha$ condensate state has been proposed as a new-type cluster state. Purpose: The aim is to reveal a dynamical process of the formation of different kinds of cluster states, in terms of a "container" aspect of clusters, in $^{16}{\rm O}$. Method: The so-called THSR wave function for the $4\alpha$ clusters is extended to inclusion of two different containers occupied independently by the $^{12}{\rm C}$ $(3\alpha)$ and $\alpha$ clusters. Results: The five $J^\pi=0^+$ states with $4\alpha$ tetrahedral shape, $\alpha+{^{12}{\rm C}}$ cluster structures, and the $4\alpha$ condensate character, are found to be represented, to good approximation, by single configurations of the extended THSR wave function with containers of appropriate shape and size. Conclusions: It is demonstrated in $^{16}{\rm O}$ that the dynamical evolution of cluster structures can be caused by size and shape evolution of a container occupied with clusters. The $\alpha$ condensate with gaslike $4\alpha$ configuration appears as a limit of the cluster formation.