Structure ofGe72,74nuclei probed with a combined analysis of heavy-ion fusion reactions and Coulomb excitation

Abstract

We study the fusion reactions of the $^{72}\mathrm{Ge}+^{72}\mathrm{Ge}$ and $^{74}\mathrm{Ge}+^{74}\mathrm{Ge}$ systems in terms of the full order coupled-channels formalism. We obtain the fusion excitation function as well as the fusion barrier distribution of these reactions using the coupling matrix suggested from the recent Coulomb excitation experiments. We compare those results with the results obtained by the coupling matrix based on the pure vibrational and rotational models. The barrier distribution for the $^{74}\mathrm{Ge}+^{74}\mathrm{Ge}$ reaction obtained with the experimental coupling matrix is in good agreement with that obtained with the vibrational model, in contrast to the rotational model. On the other hand, the calculations for $^{72}\mathrm{Ge}+^{72}\mathrm{Ge}$ system show that the fusion barrier distribution obtained with the experimental coupling matrix significantly differs from those obtained with vibrational and rotational models. Our study indicates that the shape of $^{74}\mathrm{Ge}$ is closer to spherical than to deformed, while $^{72}\mathrm{Ge}$ has a shape admixture in its ground state, which can be described by neither the vibrational nor the rotational models, as suggested by the Coulomb excitation experiments. This finding will resolve the debates concerning the structure of these nuclei.