Narrow Results

We present the tangential velocity corrections to the second-order Coulomb-modified eikonal model at the distance of closest approach. It has been applied to elastic angular distributions of the ¹⁶O+¹⁶O system at E_lab=350 and 480 MeV. The calculated results with tangential velocity show better agreements with the experimental data compared to those with asymptotic velocity. The Fraunhöfer oscillations observed in the elastic angular distributions can be explained by the strong interference between the near- and the far-side amplitudes. Airy structures can be shown by reducing the effective imaginary potential strength. It is found that the Airy minimum is more visible as the effective imaginary potential strength is reduced. Deep real potentials associated with rather weak imaginary ones are found to be essential to describe the refractive ¹⁶O+¹⁶O elastic scatterings at E_lab=350 and 480 MeV.

Using the six-parameter $S$-matrix model, we have obtained a simultaneous correct description of the $\alpha {+}^{24}$Mg elastic and inelastic scattering differential cross-sections over the energy region $E=50$–$240$ MeV, where typical nuclear rainbow and prerainbow patterns are observed. The Airy minima of the first-order have been unambiguously identified in the cross-sections for elastic scattering and inelastic scattering to the first 2${}^{+}$ state of ${}^{24}$Mg at $E=50$–145MeV. Their angular positions obey an inverse dependence on energy, which is in line with the “rainbow” interpretation of the data. Within this interpretation, the scattering matrix and the deflection function for the system $\alpha {+}^{24}$Mg at $E=50$–240MeV show physically justified smooth variations with the projectile energy.