Elastic Scattering of CARBON-14 + CARBON-12, Carbon -14 + OXYGEN-16, and CARBON-14 + OXYGEN-18.

We have carried out highly detailed studies of the elastic scattering of ^{14} C from ^{12}C, ^{16}O, and ^ {18}O, in a search for resonant phenomena in heavy-ion systems of non-zero isospin and zero spin. Angular distributions from ^{14}C+ ^{12}C and ^ {14}C+^{16}O scattering were measured at ^{14} C bombarding energies ranging from 20 to 40.3 MeV in 0.35 MeV steps. ^{14}C+ ^{18}O angular distributions were measured at ^{14}C energies from 20 to 30 MeV in 0.40 MeV steps and from 22.5 to 32.5 MeV in 2.5 MeV steps. The great variety of behavior which characterizes heavy-ion scattering is clearly illustrated by our data. The ^{14}C+^ {12}C and ^{14} C+^{16}O systems both exhibit marked gross structure in their excitation functions and deep oscillatory structure with a large backward angle rise in their angular distributions. They are in sharp contrast with the ^{14} C+^{18}O system, where structure is not apparent, and cross-sections fall steeply at larger angles and higher energies. However, only in the ^{14}C+ ^{12}C system are the excitation functions strongly fragmented by intermediate width structure. The anomalous appearance of the ^{14} C+^{12}C angular distributions near 17.5 MeV (cm) does suggest the existence of a resonant state (tentatively identified as l = 10 by phase shift analysis). In our analysis, we point out that the remarkable qualitative differences among these systems may be related to open-channel systematics. We find that general characteristics of the ^{14}C+ ^{18}O data are reproduced with a strongly absorbing optical potential model, contrary to the situation in the other two systems, where a specific mechanism, such as elastic transfer, must be invoked to account for the backward rise. We have pursued analysis with a one-step DWBA elastic transfer model which was quite successful at low energies. Its underprediction of the backward rise at higher energies provides further evidence of the importance of multi-step processes in two-nucleon transfer reactions. We have also applied recent group theoretical models of heavy-ion scattering to our data. The single -channel models involving the SO(3,2) and SO(3,1) dynamical symmetries were found to be somewhat more flexible than standard optical models, but were still not able to provide an acceptable gross description of the ^ {14}C+^{12}C and ^{14}C+^ {16}O data. However, a two-channel SO(3,1) dynamical symmetry model in which the elastic transfer amplitude is obtained as the second channel has provided very good fits to individual highly structured angular distributions and better overall reproduction of the datasets than the other models which we have studied.