Differential cross sections for the elastic scattering, single excitation ($Q=-4.43\mathrm{}$ MeV), and mutual excitation ($Q=-8.86\mathrm{}$ MeV) of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ by ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ have been measured at 14 bombarding energies in the range $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=35-63\mathrm{}$ MeV. The angular distributions extend typically from 16° to 90° c.m. The results have been analyzed with the optical model, the distorted-wave approximation, and the method of coupled equations. The optical model analysis of the elastic scattering reveals a sensitivity of the predicted cross sections at large angles to the strength and shape of the real part of the nuclear potential in the region 4 to 6 fm. The potentials predicted by the double-folding model fit the data remarkably well over the entire angular range, whereas the shallow potentials which we have explored generally fit the data only in the forwardangle region. The results thus indicate that the real potential for the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ system is more attractive in the region of 4 to 6 fm than would have been expected on the basis of previous analyses of comparable systems at lower bombarding energies.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$), $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=35-63\mathrm{}$ MeV; measured $\sigma (E,\theta )$ for elastic, single, and mutual excitation of $2^{+}$. Optical model, DWBA analyses.

• Received 19 March 1979

DOI:https://doi.org/10.1103/PhysRevC.20.655