Nuclear potentials for sub-barrier fusion and cluster decay inC14,O18+Pb208systems

Near-barrier fusion excitation functions for the $^{14}\mathrm{C}$ and $^{18}\mathrm{O}+^{208}\mathrm{Pb}$ reactions have been analyzed in the framework of the barrier-passing model using different forms of the nuclear potential and the phenomenology of a fluctuating barrier. The best-fit fusion potentials were used to estimate cluster decay probabilities from the corresponding ground states of Ra and Th (i.e., for the inverse decay process). The analysis supports the ``\ensuremath{\alpha}-decay-like'' scenario for carbon and oxygen emission from these nuclei.