Back-angle anomalies in alpha scattering: Inelastic scattering from the calcium isotopes

Cross sections for elastic and inelastic $\alpha$ scattering on ${}_{}{}^{40,42,44,48}{}_{}{}^{}\mathrm{Ca}$ have been measured to several excited states. The bombarding energy (lab) is 24 MeV for $\alpha$ +${}_{}{}^{40,42,44}{}_{}{}^{}\mathrm{Ca}$ and is 24 and 29 MeV for $\alpha$ +${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$. Particular emphasis is given to the back-angle data. In addition to the anomaly of $\alpha$ +${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ elastic scattering at backward angles previously reported by many workers anomalous features are also observed in inelastic scattering. It is found that the backward anomaly of the $\alpha$ +${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ inelastic cross sections is strongest for the $0^{+}$ states and gradually decreases with increasing spins of the final states ($1^{-}$, $3^{-}$, $5^{-}$). The only exception is the scattering to the $2^{+}$ state at 3.90 MeV, for which the cross sections exhibit a regular decrease toward backward angles. The inelastic cross sections for the ${}_{}{}^{42,44,48}{}_{}{}^{}\mathrm{Ca}$ isotopes are generally smaller at backward angles as compared to those for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. In general, the observed anomalies for inelastic scattering at back angles are in close analogy to those known for elastic scattering. An interpretation of the data and of the anomalies in terms of coupled channels is given. Both a standard optical potential and one with an angular-momentum-dependent absorption have been used in the calculations. It is found that the large differences in the cross sections at backward angles, depending on the isotope and on the spin of the residual state, can be reproduced by coupled-channel calculations when an angular-momentum-dependent absorption in the optical potential is assumed.