Unified S-matrix analysis of Airy structures in α+24Mg elastic and inelastic scattering

Abstract

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.

Analysis of α-208Pb Elastic Scattering at a Wide Energies by the S-Matrix Model

“…We present the results of the analysis of the available data on the elastic scattering of light ions 4 He on the 208 Pb nucleus in the energy range E α = 104-699 MeV, which is aimed at studying manifestations of the nuclear rainbow effect in this wide range of α-particle energies and determining the possibility of describing the differential cross-sections for 4 He scattering by heavy nuclei at intermediate energies using the S-matrix model, being an alternative to the optical model. We apply the 6-parameter model representation of the S-matrix [1], which was recently used for analyzing the 4 He scattering on light nuclei ( 12 C [2]) and 24 Mg [3]) and turned out to be successful in describing the nuclear rainbow picture of the 4 He scattering on these light nuclei at energies from 50 to 386 MeV. The S-matrix parameters for the investigated scattering cases have been obtained from analyzing the available experimental data (10 data sets) of the 4 He+ 208 Pb elastic scattering for energies 104 [5], 139 [6], 166 [7], 172 [8], 240 [9], 288, 340 [10], 386 [11], 480 and 699 [10] MeV.…”

“…The considered cross-sections are characterized by pronounced refraction scattering pictures (see Figs. [1][2][3][4][5][6][7][8][9][10]. In general, for the scattering of 4 He on this heavy nucleus a manifestation of the nuclear rainbow scattering is observed for all considered energies, according to the behavior of the deflection function.…”

“…Consequently, we obtain additional information about the inner nucleus structure by analyzing the differential crosssection. The rainbow scattering effect (which plays an essential role in nuclear collisions at intermediate energies) is also observed in the elastic scattering of 3 H, 3 He, 6 Li, 9 Be, 11 B, 12 C etc. by light and intermediate nuclei [2].…”

“…Further, we obtain a broad maximum, after which the cross-section decreases smoothly in the region of large scattering angles. Such a crosssection behavior is typically interpreted as a rainbow scattering [1][2][3]. However, while the energy of incident alphaparticles is increasing, the rainbow maximum becomes less pronounced, and the cross-section in the region of large angles is rapidly decreasing because it is determined by the far-side part of scattering amplitude, corresponding to the scattering from the far side of the target nucleus relative to the detector.…”

S-matrix Description of Refractive Effects in One-nucleon Stripping Reactions Induced by \(\alpha \)-particles on \(^{28}\)Si

“…Parametrization [4] was taken as S-matrices for the entrance and exit channels since it turned out to be very successful in describing the nuclear rainbow pattern and refractive patterns with Airy minima (see, e.g., Refs. [3,14]). The S-matrix parameters have been derived from the analysis of the elastic scattering data for both entrance and exit channels.…”