$\alpha$ clustering in ${}^{28}\mathbf{Si}$ probed through the identification of high-lying $0^{+}$ states

Background: Aspects of the nuclear structure of light $\alpha$-conjugate nuclei have long been associated with nuclear clustering based on $\alpha$ particles and heavier $\alpha$-conjugate systems such as ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$. Such structures are associated with strong deformation corresponding to superdeformed or even hyperdeformed bands. Superdeformed bands have been identified in ${}^{40}\mathrm{Ca}$ and neighboring nuclei and find good description within shell model, mean-field, and $\alpha$-cluster models. The utility of the $\alpha$-cluster description may be probed further by extending such studies to more challenging cases comprising lighter $\alpha$-conjugate nuclei such as ${}^{24}\mathrm{Mg}, {}^{28}\mathrm{Si}$, and ${}^{32}\mathrm{S}$.

Purpose: The purpose of this study is to look for the number and energy of isoscalar $0^{+}$ states in ${}^{28}\mathrm{Si}$. These states are the potential bandheads for superdeformed bands in ${}^{28}\mathrm{Si}$ corresponding to the exotic structures of ${}^{28}\mathrm{Si}$. Of particular interest is locating the $0^{+}$ bandhead of the previously identified superdeformed band in ${}^{28}\mathrm{Si}$.

Methods: $\alpha$-particle inelastic scattering from a ${}^{\mathrm{nat}}\mathrm{Si}$ target at very forward angles including $0^{\circ }$ has been performed at the iThemba Laboratory for Accelerator-Based Sciences in South Africa. Scattered particles corresponding to the excitation energy region of 6 to 14 MeV were momentum-analysed in the K600 magnetic spectrometer and detected at the focal plane using two multiwire drift chambers and two plastic scintillators.

Results: Several $0^{+}$ states have been identified above 9 MeV in ${}^{28}\mathrm{Si}$. A newly identified 9.71 MeV $0^{+}$ state is a strong candidate for the bandhead of the previously discussed superdeformed band. The multichannel dynamical symmetry of the semimicroscopic algebraic model predicts the spectrum of the excited $0^{+}$ states. The theoretical prediction is in good agreement with the experimental finding, supporting the assignment of the 9.71-MeV state as the bandhead of a superdeformed band.

Conclusion: Excited isoscalar $0^{+}$ states in ${}^{28}\mathrm{Si}$ have been identified. The number of states observed in the present experiment shows good agreement with the prediction of the multichannel dynamical symmetry.

Figure 1

(Top) Background-subtracted ${}^{28}\mathrm{Si}(\alpha ,{\alpha }^{\prime }){}^{28}\mathrm{Si}$ spectrum at $0^{\circ }$ with combined fit (solid line). (Middle) ${}^{28}\mathrm{Si}(\alpha ,{\alpha }^{\prime }){}^{28}\mathrm{Si}$ spectrum for the $2^{\circ } –3^{\circ }$ angle bite with combined fit (solid line). (Bottom) ${}^{28}\mathrm{Si}(\alpha ,{\alpha }^{\prime }){}^{28}\mathrm{Si}$ spectrum for the $3^{\circ }–4^{\circ }$ angle bite with combined fit (solid line). Prominent states with known energies and spin-parities have been identified in the spectra.

Figure 2

Spectra for the (top) 4–$5^{\circ }$ and (bottom) 5–$6^{\circ }$ angle ranges with combined fit.

Figure 3

Differential cross sections for states (a) 9.305-MeV $0^{+}$ state in ${}^{24}\mathrm{Mg}$, (b)–(d) states in ${}^{28}\mathrm{Si}$. The energies and $J^{\pi }$ assignments of the state A, C, and D are taken from literature [14]. State B is new. The angle uncertainty for each point corresponds to the angle bite covered. DWBA curves calculated with parameter set II (solid line) averaged over the angle ranges are plotted for $\ell =0$ and $\ell =1$ states—for the 9.71-MeV $0^{+}$ state the DWBA curve for parameter set I is also plotted (dashed line).

Figure 4

As Fig. 3 for the additional $0^{+}$ states in ${}^{28}\mathrm{Si}$. The 6.691-MeV state is the $0_3^{+}$ state in ${}^{28}\mathrm{Si}$ and does not fall on the focal plane for the $0^{\circ }$ data. Table 1 gives more details as to the properties of the states shown.

Figure 5

The spectra of the $0^{+}$ states in the ${}^{28}\mathrm{Si}$ nucleus and in its ${}^{24}\mathrm{Mg}+{}^4\mathrm{He}$ and ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ clusterizations, as predicted by the Hamiltonian of the multichannel dynamical symmetry [7]. The states are characterised by the $n(\lambda ,\mu )K^{\pi }$ quantum numbers, where $n$ is the major shell excitation, and $(\lambda ,u)$ refers to the SU(3) representation, i.e., the quadrupole deformation.

Figure 6

Comparison of the ${}^{24}\mathrm{Mg}+{}^4\mathrm{He} 0^{+}$ spectra from the theoretical prediction (of Fig. 5) and the experimental observation. The energy-window of the present experiment is indicated by the dotted lines in both panels. In the experimental part the solid lines show the observed resonances of the present work, the dotted Y-shaped lines are the states from the ${}^{24}\mathrm{Mg}+{}^4\mathrm{He}$ measurements [23] which are not resolved in the present experiment. The dashed lines correspond to known low-lying $0^{+}$ states which were not measured at 0° in the present experiment.