“Container” evolution for cluster structures in ${}^{16}\mathrm{O}$

Background: $\alpha +{}^{12}\mathrm{C}$ clustering in ${}^{16}\mathrm{O}$ 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 ${}^{16}\mathrm{O}$.

Method: The so-called THSR wave function for the $4\alpha$ clusters is extended to inclusion of two different “containers” occupied independently by the ${}^{12}\mathrm{C}\left(3\alpha \right)$ and $\alpha$ clusters.

Results: The five $J^{\pi }=0^{+}$ states with $4\alpha$ tetrahedral shape, $\alpha +{}^{12}\mathrm{C}$ 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 ${}^{16}\mathrm{O}$ 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.

Figure 1

Schematic representation of the eTHSR wave function, in which the two “containers” of the $3\alpha$ and $\alpha$ clusters are characterized by the parameters ${\mathbf{B}}_1$ and ${\mathbf{B}}_2$, respectively.

Figure 2

Energy spectra of the low-lying $J^{\pi }=0^{+}$ states calculated with the extended THSR ansatzes. The corresponding observed spectrum (Expt.) [38, 39] and result by the $4\alpha$ OCM [9] are also shown. The numbers are rms radii in a unit of fm.

Figure 3

Contour maps of the squared overlaps between the $0_I^{+}$ (a), $0_{II}^{+}$ (b), $0_{III}^{+}$ (c), $0_{IV}^{+}$ (d), and $0_V^{+}$ (e) states, and the single extended deformed THSR wave functions, in two-parameter space ${\beta }_{2x}={\beta }_{2y}$ and ${\beta }_{2z}$, in which ${\mathbf{\beta }}_1$ parameter values are fixed at optimal ones, denoted by $\otimes$, so that the maxima in four-parameter space ${\beta }_{1x}={\beta }_{1y},{\beta }_{1z},{\beta }_{2x}={\beta }_{2y},{\beta }_{2z}$ appear in these figures. The maximum positions are denoted by $\times$. Red dotted contour lines are in a step of 0.01 and black solid ones are in a step of 0.1.