We present the results of the [Formula: see text]-matrix description of the [Formula: see text] elastic and inelastic scattering differential cross-sections between 40 and 240 MeV with allocation of Airy minima of various orders. The first-order Airy minima have been unambiguously identified in the differential cross-sections for elastic scattering and inelastic scattering to the first [Formula: see text] state of [Formula: see text] at energies [Formula: see text] MeV, and the second-order Airy minima — at [Formula: see text] MeV. The angular positions of these minima obey an inverse dependence on energy. The intensities of nuclear refraction and absorption also obey the same energy dependence.

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Using the six-parameter [Formula: see text]-matrix model, we have obtained a simultaneous correct description of the [Formula: see text]Mg elastic and inelastic scattering differential cross-sections over the energy region [Formula: see text]–[Formula: see text] 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[Formula: see text] state of [Formula: see text]Mg at [Formula: see text]–145[Formula: see text]MeV. 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 [Formula: see text]Mg at [Formula: see text]–240[Formula: see text]MeV show physically justified smooth variations with the projectile energy.

The patterns typical of Fraunhofer and Fresnel diffraction scattering and refraction (rainbow) scattering are discussed. We extract different interference contributions responsible for the characteristic structural features of the analyzed scattering patterns by means of the S-matrix approach.