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The $\alpha$ cluster states are discussed in a model frame of extendedquantum molecular dynamics. Different alpha cluster structures are studied indetails, such as $^8$Be two-$\alpha$ cluster structure, $^{12}$C trianglestructure, $^{12}$C chain structure, $^{16}$O chain structure, $^{16}$O kitestructure, and $^{16}$O square structure. The properties studied, include asthe width of wave packets for different $\alpha$ clusters, momentumdistribution, and the binding energy among $\alpha$ clusters. It is alsodiscussed how the $\alpha$ cluster degree of freedom affects nuclear collectivevibrations. The cluster configurations in $^{12}$C and $^{16}$O are found tohave corresponding characteristic spectra of giant dipole resonance (GDR), andthe coherences of different $\alpha$ clusters's dipole oscillation aredescribed in details. The geometrical and dynamical symmetries of$\alpha$-clustering configurations are responsible for the number and centroidenergies of peaks of GDR spectra. Therefore, the GDR can be regarded as aneffective probe to diagnose different $\alpha$ cluster configurations in lightnuclei.

Dipole oscillation modes in light $\alpha$-clustering nuclei