Theoretical investigation of α -like quasimolecules in heavy nuclei

Abstract

Quasimolecular $\ensuremath{\alpha}$-like ground rotational bands were evidenced a long time ago in light nuclei, but they cannot be detected in heavy nuclei due to large Coulomb barriers. In order to search for rotational bands built on excited states in these nuclei, we investigate the shape of an $\ensuremath{\alpha}$-nucleus quasimolecular potential matched to a realistic external $\ensuremath{\alpha}$-daughter interaction by using as input data $\ensuremath{\alpha}$-decay widths. It turns out that its Gaussian length parameter lies in a narrow interval, ${b}_{0}\ensuremath{\in}[0.6,0.8]$ fm, and the equilibrium radius is slightly larger than the predicted Mott transition point from nucleonic to the $\ensuremath{\alpha}$-cluster phase in finite nuclei, confirming that $\ensuremath{\alpha}$ clusters are born on the nuclear surface at low densities. We point out that the $\ensuremath{\alpha}$ emitters above magic nuclei have the largest spectroscopic factors ${S}_{\ensuremath{\alpha}}\ensuremath{\sim}10%$. In addition, we predict that for nuclei with ${b}_{0}g0.75$ fm, the first excited vibrational resonant state in the quasimolecular potential is close to the Coulomb barrier and therefore the rotational band built on it can be evidenced by the structure of the $\ensuremath{\alpha}$-scattering cross section versus energy. Moreover, its detection by a highly sensitive $\ensuremath{\gamma}$-ray beam produced by laser facilities would provide an additional proof for the existence of $\ensuremath{\alpha}$ molecules in heavy nuclei.