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

Abstract

Angular distributions for the $^{16}\mathrm{O}(p,{p}^{\ensuremath{'}})^{16}\mathrm{O}$ reaction leading to the ${J}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ state at 8.88 MeV and the doublet of states at 6.05 MeV (${0}^{+}$) and 6.13 MeV (${3}^{\ensuremath{-}}$) 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 (${2}^{\ensuremath{-}}$) state can occur only through the spin-dependent part ${V}_{10}={V}_{\ensuremath{\sigma}}f(r){\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}}_{p}$ of the effective two-nucleon interaction. The experimental angular distributions were compared with DWA calculations assuming $f(r)$ has a Yukawa shape with a range of 1.0 F. Normalization to the measured cross sections determined the strength ${V}_{\ensuremath{\sigma}}$, which was found to decrease rapidly from a magnitude of 53 MeV to about 23 MeV between ${E}_{p}=17.0$ MeV and ${E}_{p}=30.1$ MeV, and then to decrease slowly to about 16 MeV at ${E}_{p}=46.1$ MeV. The shape of the experimental angular distributions for the inelastic scattering to the ${2}^{\ensuremath{-}}$ 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 ${2}^{\ensuremath{-}}$ 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.