Nontrivial origin for the large nuclear radii of dripline oxygen isotopes

The anomalous large radii are exotic phenomena observed around the neutron dripline. Around the neutron dripline, the weak binding of the last bound neutron(s) causes the drastic increase of the radius, which is called the neutron halo structure. Although the nucleus ${}^{24}\mathrm{O}$ is located at the dripline of oxygen isotopes, the separation energies of one and two neutron(s) are 4.19 MeV and 6.92 MeV, respectively. In spite of this sufficient binding, the enhancement of the matter radius is observed. In this study, we microscopically describe the structure change of the ${}^{22}\mathrm{O}$ core in ${}^{24}\mathrm{O}$ and explain the observed large radius based on the cluster model. Two degrees of freedom for the large radius, the relative distances among four $\alpha$ clusters and the size of each $\alpha$ cluster, are examined, where the Tohsaki interaction, which has finite range three-body terms, is employed. The nucleus ${}^{22}\mathrm{O}$ has smaller $\alpha \text{−}\alpha$ distance compared with ${}^{16}\mathrm{O}$ owing to the gluelike effect of six valence neutrons around four $\alpha$ clusters. When two neutrons are added at the center of ${}^{22}\mathrm{O}$, the expansion of each $\alpha$ cluster is energetically more favored than increasing the $\alpha \text{−}\alpha$ distances for reducing the kinetic energy of the neutrons. The calculated rms matter radii of ${}^{22}\mathrm{O}$ and ${}^{24}\mathrm{O}$ are 2.75 fm and 2.92 fm, respectively. Although these are slightly smaller than the experimental values, the jump at ${}^{24}\mathrm{O}$ from ${}^{22}\mathrm{O}$ is reproduced.

Figure 1

Schematic figure for ${}^{24}\mathrm{O}$. Large blue spheres show the four $\alpha$ clusters with the relative distance of $R$ (fm) for the ${}^{16}\mathrm{O}$ core. The small red spheres are di-neutron clusters with the relative distance of $R^{\prime }$ (fm), which are changed to quasiclusters based on AQCM. One more di-neutron (small green sphere) is added at the origin corresponding to ${\left(2s\right)}^2$.

Figure 2

The principal quantum number of ${}^{22}\mathrm{O}$ and ${}^{24}\mathrm{O}$ as a function of $\alpha \text{−}\alpha$ distance for the four $\alpha$ clusters $(R$ in Fig. 1). The size parameters $\nu$ in Eq. (9) for ${}^{22}\mathrm{O}$ and ${}^{24}\mathrm{O}$ are 0.$18{\mathrm{fm}}^{-2}$ and 0.$16{\mathrm{fm}}^{-2}$, respectively.

Figure 3

Expectation values of one-body spin-orbit operator ${\sum }_i{\mathbf{l}}_{\mathbf{i}}·{\mathbf{s}}_{\mathbf{i}}$ of ${}^{20}\mathrm{O}$ and ${}^{24}\mathrm{O}$ as a function of $\mathrm{\Lambda }$ value at the limit of $R,R^{\prime }\to 0$. The size parameters $\nu$ in Eq. (9) for ${}^{22}\mathrm{O}$ and ${}^{24}\mathrm{O}$ are 0.$18{\mathrm{fm}}^{-2}$ and 0.$16{\mathrm{fm}}^{-2}$, respectively.

Figure 4

The $0^{+}$ energies of ${}^{16}\mathrm{O},{}^{20}\mathrm{O}$, and ${}^{24}\mathrm{O}$ as a function of $\alpha \text{−}\alpha$ distance for the four $\alpha$ clusters $(R$ in Fig. 1). The size parameter $\nu$ of the single-part wave function in Eq. (9) is chosen so as to obtain the lowest energy: $\nu =0.23{\mathrm{fm}}^{-2}$ for ${}^{16}\mathrm{O},\nu =0.18{\mathrm{fm}}^{-2}$ for ${}^{22}\mathrm{O}$, and $\nu =0.16{\mathrm{fm}}^{-2}$ for ${}^{24}\mathrm{O}$.

Figure 5

The size parameter $\nu$ dependence for the $0^{+}$ energy of ${}^{24}\mathrm{O}$ as a function of $\alpha \text{−}\alpha$ distance for the four $\alpha$ clusters $(R$ in Fig. 1).