Elastic angular distributions for ${}_{}{}^{12}{}_{}{}^{}$C${+}^{12}$C and ${}_{}{}^{16}{}_{}{}^{}$O${+}^{12}$C have recently been measured in the c.m. energy range between 70 and 700 MeV. The wide angular range covered by the measurements exhibits, in every case, a distinct Fraunhofer crossover followed at larger angles by a farside-dominated ‘‘smooth falloff,’’ whose appearance is a clear sign that these systems (unlike heavier ones) are surface transparent. A recent optical-model analysis of these data has produced a family of refractive ($V_0$/$W_0$≳6) potentials common to all the angular distributions, whose analysis is the subject of this and the following paper. The present paper identifies key interference dips in the farside cross sections which signify the occurrence of deeply penetrating trajectories. These dips are responsible for reducing or even eliminating potential ambiguities, and the following paper exhibits and identifies the interfering farside trajectories via a semiclassical analysis of the optical potential amplitudes. The net result is an unusually clear and detailed physical understanding of highly complex angular distributions.

• Received 4 January 1988

DOI:https://doi.org/10.1103/PhysRevC.38.673