Low-energy cluster vibrations in N = Z nuclei

Significant transition strength in light $\alpha$-conjugate nuclei at low energy, typically below 10 MeV, has been observed in many experiments. In this work the isoscalar low-energy response of N=Z nuclei is explored using the Finite Amplitude Method (FAM) based on the microscopic framework of nuclear energy density functionals. Depending on the multipolarity of the excitation and the equilibrium deformation of a particular isotope, the low-energy strength functions display prominent peaks that can be attributed to vibration of cluster structures: $\alpha$+${}^{12}$C+$\alpha$ and $\alpha$+${}^{16}$O in ${}^{20}$Ne, ${}^{12}$C+${}^{12}$C in ${}^{24}$Mg, 4$\alpha$+${}^{12}$C in ${}^{28}$Si, etc. Such cluster excitations are favored in light nuclei with large deformation.