Angular distributions for $\alpha$ particle elastic scattering by ${}_{}{}^{40,44}{}_{}{}^{}\mathrm{Ca}$ and excitation of the 3.73 MeV $3^{-}$ collective state of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ were measured for incident energies ranging from 40 to 62 MeV. An extensive optical model analysis of these elastic scattering cross sections and other available data, using squared Woods-Saxon form factors, results in potentials with fixed geometry for both real and imaginary parts and depths with smooth energy behavior over a broad incident energy range. These results are discussed in the frame of the semi-classical approximation developed by Brink and Takigawa. The sensitiveness of the calculated elastic scattering cross sections to the real part of the potentials as a function of the projectile-target distance has been investigated by means of a notch test. Distorted-wave Born-approximation calculations for the excitation of the 3.73 MeV $3^{-}$ state of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are presented.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(\alpha , \alpha )(\alpha , {\alpha }^{\prime })$, $E_{\alpha }=40, 42, 44, 46, 48, 50, 54, 58, 62$ MeV; ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}(\alpha , \alpha )$ $E_{\alpha }=40, 42, 46, 48, 50, 54, 58$ MeV; measured $\sigma \left(\theta \right)$, $110°<~\theta <~176°$; deduced optical model parameters and ${\beta }_3$ for the 3.73 MeV $3^{-}$ state of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$; enriched targets ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$.

• Received 27 January 1978

DOI:https://doi.org/10.1103/PhysRevC.18.1237