We show that the concept of internal and barrier waves based on a semiclassical picture is useful for understanding intuitively the origin of oscillations in fusion excitation functions. The mechanism which causes the oscillations in the excitation function for the α${+\mathrm{}}^{40}$Ca system is investigated by decomposing the S matrix into its internal and barrier components: The S matrices and the fusion cross sections are calculated by using an optical model with a deep real potential which reproduces the fusion data well. It is shown that interference between internal and barrier waves is responsible for the oscillations of the fusion excitation function: The broad peaks are due to destructive interference which satisfies a resonance condition, while the valleys of the oscillations are due to constructive interference. The internal and barrier wave interpretation is fully consistent with the quantum mechanical description which associates the oscillations of the fusion excitation function with broad resonances in the α${+\mathrm{}}^{40}$Ca cluster structure, i.e., with higher nodal states of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ at high excitation energy.

• Received 9 December 1986

DOI:https://doi.org/10.1103/PhysRevC.36.966