Analysis of Nuclear Scattering by Regge Poles

The validity and usefulness of the complex angular-momentum formulation in nuclear scattering are investigated by studying the elastic scattering of $\alpha$ particles by ${\mathrm{He}}^4$, ${\mathrm{C}}^{12}$, and ${\mathrm{O}}^{16}$ in terms of the Regge trajectories through suitable Regge-type representations for the $S$ matrix. The trajectories are obtained from the resonant levels of the compound nuclei, and residues are calculated by imposing unitarity on the Regge-type representations for the $S$ matrix. The differential cross sections obtained by this method are compared with those obtained by experiment and by the Ackhiezer-Pomeranchuk-Blair-McIntyre model with resonant phase shifts. In order to establish the merit of the Regge-pole approach, cross sections are calculated in terms of the poles of the $S$ matrix in the momentum plane and compared with the results obtained by using the complex angular-momentum formulation. These studies provide an interesting method for the analysis of nuclear scattering.