Using data obtained through simultaneous measurements of $(\overrightarrow{p},p^{\prime })$ spin-transfer observables and $\left(\overrightarrow{p}{,p}^{\prime }\gamma \right)$ coincident spin observables, we have made a model-independent determination of the complete scattering amplitude for the 15.11 MeV, $1^{+},$ $T=1\mathrm{}$ state in ${}^{12}\mathrm{C}$ at an incident proton energy of 200 MeV, for four proton scattering angles ranging from ${\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}=5.5\mathrm{}°–16.5°.$ At each angle, 16 different observables were determined, whereas only 11 independent quantities are required to specify the transition amplitude for this state. It had been shown previously that the set of observables measured span the allowed space; hence the system is overdetermined, which allowed us to extract, in a model-independent fashion, each of the individual spin-operator amplitudes that characterize the reaction. Additional insight into the physical mechanisms that drive this transition is obtained by mapping out the momentum-transfer dependence of these amplitudes. We also compare the magnitudes and phases determined for each of the spin-operator amplitudes to the predictions of calculations performed in both relativistic and nonrelativistic frameworks, and discuss the physics content of these comparisons.

• Received 8 April 1999

DOI:https://doi.org/10.1103/PhysRevC.61.014601