$4\alpha$ linear-chain state produced by ${}^9\mathrm{Be}+{}^9\mathrm{Be}$ collisions

The linear-chain (LC) structure provides significant insights into quantum many-body systems with geometric configurations. In this study, $4\alpha +2n$ LC was assessed in ${}^{18}\mathrm{O}$. The excitation energies, moment of inertia, and $\alpha$- and ${}^9\mathrm{Be}$-decay widths of the LC states were predicted using antisymmetrized molecular dynamics. We predict that there are two $4\alpha$ LC bands, $K^{\pi }=0^{+}$ and $K^{\pi }=3^{-}$, which exhibit different decay properties. We demonstrate that the $K^{\pi }=3^{-}$ LC states can be verified by the head-on ${}^9\mathrm{Be}+{}^9\mathrm{Be}$ collision experiments because their states exhibited large decay widths in the ${}^9\mathrm{Be}+{}^9\mathrm{Be}$ channel.

Figure 1

Schematic illustration of the $4\alpha$ LCs constructed by (a) antiparallel and (b) parallel alignments with respect to the $j_z$ of the valence neutrons in ${}^9\mathrm{Be}$. The black arrows indicate $j_z=+3/2$ orbit of the valence neutron, while the red arrow indicates $j_z=-3/2$.

Figure 2

Calculated energies above the ${}^9\mathrm{Be}+{}^9\mathrm{Be}$ threshold of the LC states as functions of angular momenta. The energy is relative to 23.64 MeV.

Figure 3

Density distributions of the intrinsic states of the LC bands. The contour lines show the proton density distributions, and the color plots show the valence neutron orbits. (a) shows the intrinsic state of the positive-parity band, in which two valence neutrons occupy negative-parity orbits with $j_z=\pm 3/2$. (b1) and (b2) show the intrinsic state of the negative-parity band, in which a valence neutron occupies the negative-parity orbit with $j_z=3/2$ (b1) and the other occupies the positive-parity orbit with $j_z=3/2$ (b2).

Figure 4

Calculated overlaps between the ${}^9\mathrm{Be}+{}^9\mathrm{Be}$ Brink and AMD wave functions. ${\mathrm{\Psi }}_{LC}^{+}$ and ${\mathrm{\Psi }}_{LC}^{-}$ correspond to Fig. 3 and (b), respectively.