The $\alpha$ cluster states are discussed in a model frame of extended quantum molecular dynamics. Different $\alpha$ cluster structures are studied in detail, such as ${}^8\mathrm{Be}$ two-$\alpha$ cluster structure, ${}^{12}\mathrm{C}$ triangle structure, ${}^{12}\mathrm{C}$ chain structure, ${}^{16}\mathrm{O}$ chain structure, ${}^{16}\mathrm{O}$ kite structure, and ${}^{16}\mathrm{O}$ square structure. The properties studied include the width of wave packets for different $\alpha$ clusters, momentum distribution, and the binding energy among $\alpha$ clusters. We also discuss how the $\alpha$ cluster degree of freedom affects nuclear collective vibrations. The cluster configurations in ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ are found to have corresponding characteristic spectra of giant dipole resonance (GDR), and the coherences of different $\alpha$ clusters' dipole oscillations are described in detail. The geometrical and dynamical symmetries of $\alpha$-clustering configurations are responsible for the number and centroid energies of peaks of GDR spectra. Therefore, the GDR can be regarded as an effective probe to diagnose different $\alpha$ cluster configurations in light nuclei.

• Received 8 March 2016
• Revised 14 May 2016

DOI:https://doi.org/10.1103/PhysRevC.94.014301