Spin Flip in the Inelastic Scattering of Protons

Proton spin-flip probabilities and differential inelastic scattering cross sections were measured over a large angular region for the following $2^{+}$ excitations: 4.44 MeV in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ at 12, 13, 14, 15, and 20 MeV; 1.45 MeV in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ at 9.25, 10.46, 15, and 20 MeV; 1.33 MeV in ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$ at 10.5 and 14 MeV; and 1.34 MeV in ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$ at 10.5 and 14 MeV. The results were analyzed in the distorted-wave Born approximation, with collective-model form factors derived from the optical-model potential. The deformed spin-dependent part of the coupling potential was of the full Thomas form, and the data are best described when ${{\beta }_2}^{\mathrm{SO}}>{\beta }_2$. Good fits are obtained for elastic polarization data (obtained elsewhere) when the depth of the spin-orbit potential is determined from spin-flip probability measurements.