Spin and isospin transfer in theC12(π+,π+′) reaction

Inelastic scattering cross sections from ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ were measured for the 12.7 MeV ($1^{+}$;0), 15.1 MeV ($1^{+}$;1), and 16.1 MeV ($2^{+}$;1) levels for positive pion beam energies of 100, 116, 140, 160, 180, 200, 230, 260, and 291 MeV. Clearly oscillatory angular distributions were measured for the $1^{+}$ states, and these are shown to be explained by very general considerations of the scattering amplitudes. The 16.1 MeV data show little structure at the lower beam energies, but the falling angular dependence at the higher beam energies is very like that observed for the 4.4 MeV ($2^{+}$;0) state. A prediction for the ratio of the $T=0\mathrm{}$ and $T=1\mathrm{}$ $1^{+}$ cross sections is derived from a specific two-step calculation, and found to agree with the data at the 3-3 resonance.