Neutron and proton transition densities from 32,34S(p,p') at Ep=318 MeV. II. Neutron densities for 34S.

Differential cross sections and analyzing powers for low-lying states of $^{34}\mathrm{S}$ were measured using 318 MeV protons. Neutron transition densities for the ${2}_{1}^{+}$ and ${2}_{2}^{+}$ states were fitted to the data using general expansions which permit evaluation of uncertainties due to statistical and normalization errors, penetrability and distortion, and incompleteness in momentum space. We find that the experimental densities agree well with the shell model for the first ${2}^{+}$ state, but that the neutron density for the second ${2}^{+}$ state is distinctly different in shape. We also find ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$=+0.27(6) for the ${2}_{2}^{+}$ state, in qualitative agreement with electromagnetic results for A=34 but in marked disagreement with the shell-model prediction of ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$=-0.61. A detailed analysis of earlier data for 650 MeV, originally described as qualitatively consistent with the shell model, is also presented and shows that these data are more consistent with the present results. The shape of the isoscalar density for the ${2}_{2}^{+}$ state of $^{34}\mathrm{S}$ cannot be reproduced with the sd shell, supplemented by surface-peaked core polarization, but can be reproduced if an empirical (1f${)}^{2}$ contribution is admitted. Shell-model calculations were performed for other ${2}^{+}$ and ${4}^{+}$ states of $^{34}\mathrm{S}$, but give cross sections well below the (p,p') data for all but the lowest ${2}^{+}$ state. The data for the lowest ${1}^{\mathrm{\ensuremath{-}}}$, ${3}^{\mathrm{\ensuremath{-}}}$, and ${5}^{\mathrm{\ensuremath{-}}}$ states in both $^{34}\mathrm{S}$ and $^{32}\mathrm{S}$ are very similar.