Some years ago, Drisko et al. suggested that the discrete ambiguity often encountered for elastic scattering optical potentials could be understood as being due to the interior or small-l S-matrix elements for two ‘‘equivalent’’ potentials differing in phase by 2π, l-by-l. We point out that the absence of this phase change for peripheral partial waves is equally essential, and suggest that a deeper understanding of the ambiguity may be achieved by viewing it as a consequence of a farside interference between interior and peripheral partial waves. It is this interference which produces the broad ‘‘Airy maxima’’ of a nuclear rainbow, and we show that a Drisko-type phase-shift increment ${\mathrm{\delta }}_{\mathit{l}}$→(${\mathrm{\delta }}_{\mathit{l}}$+π) for low-l phases relative to the high-l ones is exactly what is needed to shift a farside rainbow pattern by one Airy maximum, thus providing an equivalent ‘‘rainbow-shift’’ interpretation of the discrete ambiguity. The physical importance of both interpretations lies in the fact that the existence of discrete ambiguities (as well as of nuclear rainbows) is explicit evidence for low-l transparency in nucleus-nucleus collisions. The essential role played by low partial waves explains why peripheral reactions have generally not proven helpful in resolving this ambiguity.

• Received 20 February 1990

DOI:https://doi.org/10.1103/PhysRevC.43.1140