Elastic and inelastic proton differential cross sections for excitation of the following levels of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$: $2_1^{+}$(4.43 MeV), $4_1^{+}$(14.08 MeV), $0_2^{+}$(7.65 MeV), and $3_1^{-}$(9.64 MeV) have been measured at three incident energies between 30 and 40 MeV. The data have been described by coupled channel calculations and form factors obtained by coupling surface vibrations to static deformations. The reproduction of the $0_2^{+}$ state data, if this state is assumed to be a $\beta$-vibrational state, requires a quadrupole $\beta$-vibrational amplitude which is 57% of the static quadrupole deformation and a mixing of the breathing mode of the nucleus with an amplitude that would correspond to about 1% of the $E0\mathrm{}$ energy weighted sum rule. For the $3_1^{-}$ state it is found that the performed calculations are sensitive to the $K$ projection, with the angular distribution of the $3_1^{-}$ state being better fitted assuming $K^{\pi }=3^{-}$ band. Coupled channel calculations using microscopic form factors obtained from wave functions generated using the resonating group method have also been performed and are compared to the experimental data.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(p,p′), $E_{\mathrm{p}}=29.95, 35.2, \mathrm{and} 39.9$ MeV; measured $\sigma (E_x, \theta )$; compared with coupled channel analyses using rotor-vibrator model and microscopic $3-\alpha$ cluster wave functions; deduced coupling parameters.

• Received 13 June 1983

DOI:https://doi.org/10.1103/PhysRevC.28.1443