Inelastic Scattering of Protons fromO16and the Spin-Dependent Part of the Effective Interaction

Angular distributions for the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p,p^{\prime }){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ reaction leading to the $J^{\pi }=2^{-}$ state at 8.88 MeV and the doublet of states at 6.05 MeV ($0^{+}$) and 6.13 MeV ($3^{-}$) have been measured at 23.4, 24.5, 27.3, 30.1, 34.1, 36.8, 39.7, 43.1, and 46.1 MeV. In the distorted-wave approximation (DWA) with central forces, the transition to the unnatural-parity ($2^{-}$) state can occur only through the spin-dependent part $V_{10}=V_{\sigma }f\left(r\right)\mathrm{}{\overrightarrow{\sigma }}_i·{\overrightarrow{\sigma }}_p$ of the effective two-nucleon interaction. The experimental angular distributions were compared with DWA calculations assuming $f\left(r\right)\mathrm{}$ has a Yukawa shape with a range of 1.0 F. Normalization to the measured cross sections determined the strength $V_{\sigma }$, which was found to decrease rapidly from a magnitude of 53 MeV to about 23 MeV between $E_p=17.0\mathrm{}$ MeV and $E_p=30.1\mathrm{}$ MeV, and then to decrease slowly to about 16 MeV at $E_p=46.1\mathrm{}$ MeV. The shape of the experimental angular distributions for the inelastic scattering to the $2^{-}$ state are well represented by the DWA at the lower energies, but the agreement deteriorates as the energy increases. The forward peak in the higher-energy data occurs at larger angles than the DWA prediction. The cross section calculated using a pseudopotential derived from the impulse approximation is too small by a factor of about 4 at all energies. The possible contribution of other reaction mechanisms to the cross section for scattering to the $2^{-}$ state is discussed. An analysis of the transition to the 6.1- MeV doublet is used to estimate the strength $V_c$ of the spin-isospin-independent part $V_{00}$ of the effective two-nucleon interaction. The experimental angular distributions for the 6.1- MeV doublet were also compared with the predictions of the impulse approximation.