Linear Chain Structure of Four-$\alpha$ Clusters in ${}^{16}\mathrm{O}$

We investigate the linear chain configurations of four-$\alpha$ clusters in ${}^{16}\mathrm{O}$ using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region of angular momentum ($13–18\hslash$) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia (${\hslash }^2/2\Theta \sim 0.06–0.08\mathrm{MeV}$) can exist.

Figure 1

Surface of the total nucleon density distribution for the initial twisted wave function. We chose the surface as half of the total density.

Figure 2

Total nucleon density distribution calculated using the cranking method for (a) the initial wave function, (b) the ground state, (c) the quasistable state, and (d) the four-$\alpha$ linear chain state. The isolines correspond to multiples of $0.02{\mathrm{fm}}^{-3}$. We normalize the color to the density distribution at the maximum of each plot.

Figure 3

Coefficient of the rotational energy ${\hslash }^2/2\Theta$ calculated using the cranking method versus the HF iterations with various rotational frequencies $\omega$. The symbols ($b$), ($c$), and ($d$) correspond to the density distributions given in Fig. 2.

Figure 4

Coefficient of the rotational energy ${\hslash }^2/2\Theta$ as a function of rotational frequency $\omega$. The lines correspond to the different Skyrme forces as indicated.

Figure 5

Angular momentum as a function of rotational frequency $\omega$ for the Skyrme forces. The lines with solid symbols denote the calculated results for the rigid-body moment of inertia, while the open symbols denote the results for the cranking method.

Figure 6

Calculated excitation energies of the four-$\alpha$ linear chain states with the SkI3 force versus the angular momentum. The dotted lines denote the corresponding cluster-decomposition threshold energies.