Narrow Results

We present the results of the $S$-matrix description of the ${}^4\mathrm{\text{He}}+{}^{28}\mathrm{\text{Si}}$ 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 $2^{+}$ state of ${}^{28}\mathrm{\text{Si}}$ at energies $E=40\text{–}166$ MeV, and the second-order Airy minima — at $E=40\text{–}58$ 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.

The results of calculations of differential cross-sections for $\alpha$-${}^{12}$C elastic scattering by the $S$-matrix model are presented for 10 energy values in the energy range 65MeV$\le E_{\alpha }\le$ 386MeV in a wide range of scattering angles. The behavior of various scattering characteristics as functions of the projectile energy is analyzed. It is shown that the chosen parametrization of $S$-matrix allows describing correctly the Fraunhofer oscillations of the cross-sections in the region of small scattering angles and the rainbow scattering pattern in the region of sufficiently large angles.

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.

We present a strong absorption model with an $S$-matrix in a new form of an antisymmetrized Fermi distribution for describing diffraction patterns of neutron–nucleus scattering at intermediate energies. The proposed antisymmetric $S$-matrix has a form close to the conventional one and allows to obtain exact analytical expressions for the damping factor that determines the elastic scattering amplitude and the total cross-sections for interaction, reactions and elastic scattering. The use of an antisymmetrized Fermi function instead of the usual Fermi function in successful strong absorption models basically does not notably affect the calculated nucleon–nucleus elastic scattering differential cross-sections in the intermediate energy region.

Elastic scattering of $\alpha$-particles on medium-weight nuclei ${}^{58}$Ni is analyzed in the energy range approximately from 20 to 175MeV/nucleon using the original six-parameter S-matrix model. Energy dependences of the model parameters as well as the total reaction cross-sections, nuclear rainbow angles and Fraunhofer crossover angles are studied. Behaviors of the quantum deflection function and the S-matrix modulus are investigated as well. Regular behavior of the studied quantities indicates the consistency of the model and the reliability of the obtained parameters. The results are compared to the ones obtained from the optical model. Acceptable values of ${\chi }^2∕N$ obtained in calculations by the S-matrix model demonstrate the applicability of this model in the entire considered energy range.