Signatures for Multi-$\alpha$-Condensed States

An experimental way of testing Bose-Einstein condensation of $\alpha$ clusters in the atomic nucleus is reported. The enhancement of cluster emission and the multiplicity partition of possible emitted clusters could be direct signatures for the condensed states. The barrier for the emission of clusters, such as ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}^{*}(0_2^{+})$, is calculated and compared with the barrier for the sequential emission of 2 or $3\alpha$ particles from the compound nucleus. For the calculations, a simple approach using a folded Woods-Saxon potential is used.

Figure 1

The folded potential ($V$ in the text) for ${}^{12}\mathrm{C}$ emission as a function of the distance ($R$ in the text) between the ${}^{12}\mathrm{C}$ and the ${}^{40}\mathrm{Ca}$ core. The solid, dashed, and dotted lines correspond to the condensed, cluster, and ground states of ${}^{12}\mathrm{C}$, respectively.

Figure 2

The folded potential ($V$ in the text) for the sequential emission of $\alpha$ particles as a function of the distance ($R$ in the text) between an $\alpha$ particle and the core nucleus. The solid, dotted, and dashed lines correspond to ${}^{48}\mathrm{Cr}$ (compound $1\alpha$), ${}^{44}\mathrm{Ti}$ (compound $2\alpha s$), and ${}^{40}\mathrm{Ca}$ (compound $3\alpha s$) residual nuclei, respectively.

Figure 3

The folded potential ($V$ in the text) for the emission of ${}^{40}\mathrm{Ca}$ as a function of the distance ($R$ in the text) between two ${}^{40}\mathrm{Ca}$ nuclei. The solid line and the dotted line correspond to the condensed and ground states of ${}^{40}\mathrm{Ca}$, respectively.