Scattering of 22.5-MeV Protons from Zirconium and the Symmetry Term in the Nuclear Optical Potential

Differential cross sections for the elastic scattering of 22.5-MeV protons were measured from isotopically enriched foils of ${\mathrm{Zr}}^{90}$, ${\mathrm{Zr}}^{91}$, ${\mathrm{Zr}}^{92}$, ${\mathrm{Zr}}^{94}$, and ${\mathrm{Zr}}^{96}$ over an angular range of 20 to 150°. The ratio to the Rutherford cross section exhibits a smooth decrease in the angular position of the maxima and minima as the mass of the target nucleus is increased. The magnitude of these shifts of the maxima and minima is larger than expected on the basis of previously observed 22.2 -MeV proton elastic scattering on targets over a large range of $A$ values. This larger shift in the angular position of the features is in agreement with a dependence of the real nuclear potential well depth on the nuclear symmetry parameter, $\frac{\mathrm{}(N-Z)\mathrm{}}{A}$. A detailed optical model fit to the data yields a real nuclear potential of the form, $-V=[43.4+27.8\mathrm{}\frac{\mathrm{}(N-Z)\mathrm{}}{A}]$ MeV.