Spin alignment and phase angles inC12+C12inelastic scattering

Abstract

The spin alignment $A$ and the relative phase angle $\ensuremath{\beta}$ between the $m=+2 \mathrm{and} \ensuremath{-}2$ substates populated in $^{12}\mathrm{C}$+$^{12}\mathrm{C}$(${2}_{1}^{+}$) inelastic scattering were measured over a wide range of particle scattering angles ($53\ifmmode^\circ\else\textdegree\fi{}<{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}<101\ifmmode^\circ\else\textdegree\fi{}$) and interaction energies ($15<{E}_{\mathrm{c}.\mathrm{m}.}<33$ MeV). Although the substate population parameters depend rather strongly on reaction angle, the angle-averaged alignment is markedly enhanced at energies where either broad or narrow maxima occur in $\ensuremath{\sigma}(E)$, at least below ${E}_{\mathrm{c}.\mathrm{m}.}=26$ MeV. Above that energy variations in the alignment become damped with respect to both bombarding energy and reaction angle. The relative phase $\ensuremath{\beta}(\ensuremath{\theta})$ is approximately linear in $\ensuremath{\theta}$ at most energies. For energies below ${E}_{\mathrm{c}.\mathrm{m}.}=26$ MeV corresponding to gross structure maxima in the inelastic cross sections, the measured dependence of the phase on reaction angle suggests that the reaction is dominated at these energies by individual entrance and exit channel partial waves $L$ and ${L}^{\ensuremath{'}}$, respectively, and that these are related by ${L}^{\ensuremath{'}}=L\ensuremath{-}2$. Thus a strongly aligned configuration can be associated with the maxima. At neighboring energies no evidence for such alignment was found. Calculations with the band-crossing, diffraction, distorted-wave Born approximation, and barrier-top models were compared to the measurements. None provide an adequate representation of the data.NUCLEAR REACTIONS $^{12}\mathrm{C}(^{12}\mathrm{C}, ^{12}\mathrm{C}\ensuremath{\gamma})$, ${E}_{\mathrm{lab}}=30\ensuremath{-}65$ MeV, ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}(^{12}\mathrm{C})=53\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}101\ifmmode^\circ\else\textdegree\fi{}$. Measured particle-$\ensuremath{\gamma}$ angular correlations; deduced magnetic substate alignments, phase angles; compared with model predictions.