Determination of Quadrupole Transition Amplitudes by Polarized-Deuteron Scattering

The inelastic scattering of 20-MeV vector-polarized deuterons from ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Cr}$ provides an experimental determination of sign and magnitude of the quadrupole mass transition amplitudes $〈{2_1}^{+}\mathrm{}\left|\right|\mathrm{}{Q}^m\mathrm{}\left|\right|\mathrm{}{2_1}^{+}〉$, $〈{2_2}^{+}\mathrm{}\left|\right|\mathrm{}{Q}^m\mathrm{}\left|\right|\mathrm{}{2_2}^{+}〉$, and $〈{0_1}^{+}\mathrm{}\left|\right|\mathrm{}{Q}^m\mathrm{}\left|\right|\mathrm{}{2_2}^{+}〉〈{2_2}^{+}\mathrm{}\left|\right|\mathrm{}{Q}^m\mathrm{}\left|\right|\mathrm{}{2_1}^{+}〉〈{2_1}^{+}|\times |Q^m\mathrm{}\left|\right|\mathrm{}{0_1}^{+}〉$, which correspond to the static quadrupole moments ${Q_2}_{1^{+}}$ and ${Q_2}_{2^{+}}$ and the $P_3$ interference term in the case of electromagnetic transitions.