Phenomenological analysis of elastic scattering reactions using different models

Abstract

McIntyre and Frahn-Venter three-parameter models are used to analyze the experimental data of three elastic scattering reactions α + 58 Ni, α + 116 Sn and α + 197 Au at the same incident energy of 240MeV. The different α-scattering cases have the same number of minima and maxima in their oscillatory structures of angular distribution. The increase in the mass of target nucleus leads to a smaller nuclear deflection minimum and causes the corresponding angular distribution to become smoother and with steeper slope. The Coulomb damping of Fraunhofer oscillations has an effect accompanied with the increase of mass of target nucleus. The presence of semi-classical phenomena such as Fresnel and Fraunhofer diffraction patterns etc., has been found by analyzing the experimental data of elastic scattering reactions, 16 O + 64 Zn, 32 S + 64 Ni, and 58 Ni + 27 Al at several laboratory energies. The generalised Fresnel model can fairly reproduce the angular distribution of these reactions. Excellent fitting can be obtained using Regge pole model, especially at backward angles where the data can not be recovered by the other three models. The adopted theoretical models can reasonably account for the general pattern of the data, thus allowing us to extract important parameters from elastic scattering processes. The analysis also shows that the total reaction cross section has an energy-dependent trend similar to that found by other models.

An Analysis of Heavy-Ion Elastic Scattering Processes Using Numerical Model Based on the Partial Wave Parameterised S-Matrix with Regge Pole Factor

“…In this way, it was realised that the scattering function with such properties lends the analytical formalism of normal strong absorption features. Therefore, the nuclear interaction function may be written as [18] …”

“…In particular, the total quantal deflection function is written as the sum of θ R (λ) and θ N (λ), namely [18]:…”

“…However, the far-side branch of the scattering amplitude in a region called the shadow region (at θ ≥ θ R ) is purely diffractive and is represented by the nuclear part only. The Fraunhofer diffraction nature of the scattering is embodied by the nuclear part only [1,[17][18][19]. Thus, the interference between these two components may result in Fresnel oscillation pattern.…”

“…Then, it becomes distorted such that the positively charged core moves in the direction of the field while the halo neutrons move in the opposite direction (in the centre of mass frame). In an earlier study, the molecular two-state approximation was performed to analyse the angular distributions of the systems 19 F + 16 In the present study, the available experimental angular distributions in the elastic scattering of 9,10,11 Be from 64 Zn at a laboratory energy of 27.95 MeV [34], and 4, 6, 8 He + 208 Pb at a laboratory energy of 22 MeV [35][36][37] will be analysed, using the strong absorption model of Frahn and Venter (SAM) [1,18,19]. The analysis of SAM will explain the diffractive features that occur at forward angles when the projectile has a nuclear halo structure.…”

“…This analysis will also allow the determination of several useful parameters and physical quantities, such as the grazing angular momentum Λ, the width of the ℓ-space window that contributes to elastic scattering, Δ, the nuclear phase shift, μ, the total reaction cross section σ r , etc. [17][18][19][20][21]. For an attempt to improve the fits and search for possibly existing Regge poles, which may be responsible for structures in the angular distribution, especially at backward angles, the numerical combined model will be employed using seven adjustable parameters (three SAM plus four Regge pole parameters) [17,31].…”