Shape and Compound Elastic Scattering ofαParticles byCa40, 5.0 to 12.5 MeV

Abstract

The differential cross section for the elastic scattering of $\alpha$ particles by ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ has been measured at sixteen angles between 5.0 and 12.5 MeV in 10-keV intervals. Complicated structure is seen in the excitation functions which is often as fine as the experimental resolution (<10 keV). There are many closely spaced anomalies which are substantially wider than the experimental resolution. Very broad undulations are apparent in averaged differential cross-section curves for which the averaging interval is about 0.5 MeV. The averaged data are analyzed in this work. Shape elastic scattering represented by an optical model where reaction channels are either closed or strongly inhibited does not satisfactorily describe the angular distributions at the back angles. A combination of shape and compound elastic scattering reproduces the data except at the highest energies, where reaction cross sections are becoming significant. The expression for the compound elastic contribution to the cross section is based on Hauser-Feshbach theory and statistical-model considerations. Values obtained for the real potential-well depth of the optical model (∼140 MeV) are consistent with results previously obtained at higher energies for the same number of nodes in the $s$-wave function.