Angular distributions between 3 and 110 degrees in the laboratory system were measured for the elastic scattering of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ from ${}_{}{}^{40,42,48}{}_{}{}^{}\mathrm{Ca}$ at 51.0, 49.9, and 47.2 MeV, respectively. Pronounced oscillations were observed in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ angular distribution. Weaker oscillations were observed in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ angular distributions while none were seen in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$. An optical-model analysis was performed using Woods-Saxon and folded potentials. Surface transparent potentials were found to parametrize the oscillatory structure of the forward-angle data of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. Stronger surface absorption in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{42,48}{}_{}{}^{}\mathrm{Ca}$ imaginary potentials apparently weakens or washes out any forward-angle oscillations. Optical potentials that fit forward-angle data of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ also predict oscillatory structure in the excitation function at 180°.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, $E=51\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, measured $\sigma (E,\theta =180\mathrm{}°)$. ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, $E=49.9\mathrm{}$ MeV; ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, $E=47.2\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$.

• Received 20 July 1978

DOI:https://doi.org/10.1103/PhysRevC.19.765