Trial application of the envelope method to the potential ambiguity problem

The optical potential ambiguity is a long-standing problem in the analysis of elastic scattering data. For a specific colliding system, ambiguous potential families can lead to different behaviors in the nearside and farside scattering components. By contrast, the envelope method can decompose the experimental data into two components with negative and positive deflection angles, respectively. Hence, a question arises as to whether the comparison between the calculated nearside (or farside) component and the derived positive-deflection-angle (or negative-deflection-angle) component can help analyze the potential ambiguity problem. In this study, we conducted a trial application of the envelope method to the potential ambiguity problem. The envelope method was improved by including uncertainties in the experimental data. The colliding systems of \(^{16}\) ${}^{16}$ O+ \(^{28}\) ${}^{28}$ Si at 215.2 MeV and \(^{12}\) ${}^{12}$ C+ \(^{12}\) ${}^{12}$ C at 1016 MeV were considered in the analyses. For each colliding system, the angular distribution experimental data were described nearly equally well by two potential sets, one of which is “surface transparent” and the other is refractive. The calculated angular distributions were decomposed into nearside and farside scattering components. Using the improved envelope method, the experimental data were decomposed into the positive-deflection-angle and negative-deflection-angle components, which were then compared with the calculated nearside and farside components. The capability of the envelope method to analyze the potential ambiguities was also discussed.