The oscillations observed in the experimental α${+\mathrm{}}^{40}$Ca fusion excitation function between $E_{\alpha }$=10 and 27 MeV are described within the frame of the optical model. Use is made of an existing optical potential giving a precise description of the elastic scattering data for $E_{\alpha }$>24 MeV on a broad angular range, which is extrapolated to lower incident energies. A correct description of elastic scattering experimental excitation functions between $E_{\alpha }$=12 and 18 MeV, as well as of the fusion excitation function, is achieved by using different imaginary geometries for both processes. The oscillations appearing in the calculated fusion excitation function are due to maxima in the even-l transmission coefficients, for l ranging from 6 to 12; these maxima correspond to shape resonances in the underlying potential, which are associated with states belonging to an excited positive parity band with N=14 in the α${+\mathrm{}}^{40}$Ca system. The same potential predicts an N=12 positive parity band of states whose energies are in good agreement with the ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ experimental ground state band. It is shown that the correct reproduction of the spacing between the fusion oscillations achieved here results from the use of a deep real potential, which automatically yields a decoupling between positive and negative parity bands.

• Received 27 December 1985

DOI:https://doi.org/10.1103/PhysRevC.34.1248