Nuclear-Reaction Studies with 65-MeV Alpha Particles on Zirconium

Differential cross sections for elastic and inelastic scattering and ($\alpha$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions were measured for 65-MeV alpha particles on ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$, and ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$. Excellent optical-model fits to the elastic data were obtained with four-parameter Woods-Saxon potentials having a real depth of about 35 MeV. A continuum of fits almost as good was found for a class of deeper wells. Distorted-wave predictions for all the inelastic groups studied were made with the collective model. The results were insensitive to the ambiguity in the potentials, and were quite successful for most of the groups. Where comparisons can be made, the values of the deformation parameter ${\beta }_l$ are in agreement with results from Coulomb excitation and nuclear scattering of other particles. Exploratory calculations were made for single-particle excitation for the first $2^{+}$ and $4^{+}$ levels of ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$. The ($\alpha$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) cross sections were compared with zero-range distorted-wave predictions. Good fits to the angular distributions were obtained by selection among potentials which provide fits for elastic scattering in the entrance and exit channels. Normalization of the predictions to the data yielded spectroscopic factors in generally good agreement with results from ($d, p$) and ($p, d$) measurements for $s$ and $d$ states. In making this comparison, an empirical adjustment by a factor of 17.8 was included. The predictions for $g_{\frac{7}{2}}$ states were generally too small. Spin-orbit and nonlocal corrections do not improve the agreement. Some of the discrepancy may be due to the presence of small portions of the $h_{\frac{11}{2}}$ strength in the low-lying states.