Refractive behavior in intermediate-energy alpha scattering

We report on recent $\alpha$-scattering experiments at 141.7 MeV using ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ targets. The results are compared with previous experiments on other nuclides at approximately the same energy and are used to illustrate phenomena occurring in intermediate-energy $\alpha$ scattering to which we have given the name "refractive behavior." All the elastic scattering differential cross sections exhibit the exponential-like falloff at large angles characteristic of nuclear rainbow scattering. The variation in the rainbow angle with $A$ is found to be approximately linear. In each instance it is shown that, consistent with earlier predictions, it is the data beyond the rainbow angle which make possible the elimination of the discrete ambiguities in the optical potential: For each nucleus studied, only a single family of Woods-Saxon optical potentials is found to fit the data. The real parts of the extracted potentials are characterized by well depths ranging from 108 to 118 MeV and volume integrals $\frac{J}{4A}$ ranging from 297 to 352 MeV ${\mathrm{fm}}^3$; hence they are more nearly three times the strength of nucleon-nucleus potentials at 1/4 the incident energy, rather than 4 times, as is frequently assumed. Systematic variations of the optical potentials with $A$ occur primarily in the imaginary part of the potential and are greatest for the lighter nuclei; as $A$ decreases, $W$ and $a^{\prime }$ decrease, $r_0^{}{}_{}{}^{\prime }$ increases, and the volume integral of the real part of the potential increases.