A detailed study was made on the scattering of ${\mathrm{C}}^{12}$ from ${\mathrm{C}}^{12}$ at 126 MeV in order to better understand the inelastic scattering mechanisms involved in these reactions. Earlier experiments noted four prominent peaks in the energy spectrum of the scattered particles at forward angles. One of these peaks is due to the elastic scattering and another to the excitation of the first excited state in ${\mathrm{C}}^{12}$ ($Q=-4.43\mathrm{}$ MeV). The two remaining peaks correspond to $Q$ values of -9.0±0.7 MeV and -14.0±1 MeV. Using coincidence techniques it is shown that the principal contribution to the $Q=-9\mathrm{}$ MeV peak over the range of angles studied is due to the excitation of both ${\mathrm{C}}^{12}$ nuclei to their first excited state. An angular distribution for this process is obtained and compared to a Born approximation calculation in which all parameters are determined by previous experiments. The $Q=-14\mathrm{}$ MeV peak is shown to be due to the excitation of an $\alpha$-particle unstable level in ${\mathrm{C}}^{12}$ at 14.0±0.5 MeV. Measurement of the angular distribution of the $\alpha$ particles that decay from this level to the ${\mathrm{Be}}^8$ ground state indicates that this level has spin and parity 4+. Thus, the levels most strongly excited (4.43 MeV, 2+; 14.0±0.5 MeV, 4+) in these reactions bear a strong similarity to the level sequence expected for a ground-state rotational band in ${\mathrm{C}}^{12}$. However, the shell model in L·S coupling also accounts for the observed results as the only states in ${\mathrm{C}}^{12}$ with $T=0\mathrm{}$ and $S=0\mathrm{}$ with the ${\mathrm{}\left(p\right)\mathrm{}}^8$ configuration have $L=0, 2, \mathrm{and} 4$ with relative predicted energies in agreement with our observations.

• Received 30 January 1963

DOI:https://doi.org/10.1103/PhysRev.130.2397