Elastic and inelastic scattering of 50-MeV pions fromSi28andSi30

Angular distributions of the differential cross section for elastic and inelastic scattering of 50-MeV ${\pi }^{+}$ and ${\pi }^{\mathrm{-}}$ on ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ have been measured to a relative accuracy of 5–10? We fitted the cross section of elastic ${\pi }^{+}$ and ${\pi }^{\mathrm{-}}$ scattering from ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ simultaneously with an optical model using a second-order potential of the Michigan State University form. Our best-fit parameters differ from those given previously. The ratio of the neutron and proton transition-matrix elements for the first $J^{\pi }$ ${=2\mathrm{}}^{+}$ state in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ is found from the inelastic cross section to be 1.13±0.09. For ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, the ratio is found to be 0.93±0.09, which differs significantly from the value derived from lifetime measurements on mirror nuclei.