Determination of Relative Signs of Neutron and Proton Transition Matrix Elements: Strong Cancellation Observed for theS34(0→+22+) Transition

Hadron scattering is shown to be sensitive to the relative sign of neutron and proton transition matrix elements. The relative signs for the $2_2^{+}$ states are determined to be positive for ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, and negative for ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$ on the basis of proton differential cross-section measurements at 650 and 800 MeV. Suppression of the one-step amplitude in the ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$ $2_2^{+}$ state causes the interference of one-step and multistep reactions to be experimentally apparent.