Using the six-parameter $S$ $S$ -matrix model, we have obtained a simultaneous correct description of the $α +^{24}$ $α +^{24}$ Mg elastic and inelastic scattering differential cross-sections over the energy region $E = 50$ $E = 50$ – $240$ $240$ 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 $^{24}$ $^{24}$ Mg at $E = 50$ $E = 50$ –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 $α +^{24}$ $α +^{24}$ Mg at $E = 50$ $E = 50$ –240MeV show physically justified smooth variations with the projectile energy.

Keywords:

PACS: 25.55.Ci, 24.10.Ht

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