α-nucleus potential for α-decay and sub-barrier fusion

The set of parameters for \ensuremath{\alpha}-nucleus potential is derived by using the data for both the \ensuremath{\alpha}-decay half-lives and the fusion cross sections around the barrier for reactions $\ensuremath{\alpha}+$$^{40}\mathrm{Ca}$, $\ensuremath{\alpha}+$$^{59}\mathrm{Co}$, and $\ensuremath{\alpha}+$$^{208}\mathrm{Pb}$. The \ensuremath{\alpha}-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated \ensuremath{\alpha}-decay half-lives and the fusion cross sections agreed well with the data. Fusion reactions between \ensuremath{\alpha} particles and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.