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A phenomenological method of analysis for heavy-ion elastic scattering data at intermediate energies is proposed within the framework of the optical limit approximation of the Glauber multiple scattering theory. The essential point of our method is to evaluate the NN scattering amplitude in terms of a phenomenological effective NN potential the parameters of which are varied to fit the experimental data. It is applied to analyze ¹²C–¹²C elastic scattering data in the energy range of 25–200 MeV/nucleon with a good degree of success.

Working within the framework of the Coulomb modified Glauber model and the optical limit approximation, we propose a phenomenological method of analysis for heavy-ion elastic scattering data at intermediate energies. Instead of using the commonly employed Gaussian approximation for the input NN amplitude that is deficient in some respects at low intermediate energies, we evaluate it in terms of a three parameter phenomenological NN phase shift function. The application of the method to some ¹²C-nucleus and ¹⁶O-nucleus systems shows that a very good description of the elastic scattering data at several energies can be obtained in this way. In particular, the ¹²C–¹²C elastic scattering data at 200 MeV/nucleon is very well reproduced. We also calculate the effective NN potential using the phenomenological NN phase shift function by the method of inversion. The calculated potential shows the expected behavior and is found to vary smoothly with energy.

The Frahn–Venter and McIntyre models are employed to analyze the experimental data of a set of elastic scattering reactions for heavy ions. The existence of semi-classical phenomena such as Fresnel and Fraunhofer diffraction patterns has been obtained by analyzing the experimental data of a set of elastic scattering reactions ¹²C + ²⁸Si at laboratory energies 24.0, 49.3, 70.0, 83.5, and 186.4 MeV, ¹⁶O + ²⁸Si at laboratory energies 72.0, 141.5, and 215.0 MeV, ¹⁶O + ¹⁶O at laboratory energies 145.0 and 350.0 MeV, ¹⁶O + ¹²C at laboratory energies 128.0 and 168.0 MeV; ¹²C + ¹²C at laboratory energies 89.7, 93.8, 105.0, 112.0, 117.1, 121.6, 126.7, and 158.8 MeV. The theoretical models can reasonably reproduce the general pattern of the data, thus allowing us to extract important parameters from elastic scattering processes. Deviations of some reproduced results from experimental data may be attributed to weak absorption. It is found that interpretation of the diffraction features of the data is model-independent. The values of extracted parameters, from both models, are found comparable to each other and to those of others. The correlation between the total reaction cross-section and the incident laboratory energy for each scattering is discernible and comparable with those of others.

Regge pole model is adopted to account for the angular distribution at backward angles for a set of elastic scattering processes of incident $\alpha$-particles by different isotopes of nickel ions, ${}^{58,60,62,64}$Ni, at different laboratory energies above Coulomb barrier. The reproduction of cross-sections at backward angles is preceded by an attempt to fit the experimental data at forward angles of the scattering. Three-parameter McIntyre model which is based on concept of strong absorption parametrization of the scattering matrix elements, has been employed to analyze and reproduce the experimental data of angular distribution of different elastic scattering reactions at forward angles. The three parameters extracted from McIntyre model analysis are employed as fixed entries in the fitting process of the full angle-range of angular distribution where another four free parameters are employed using the Regge pole model. Diffractive features observed in the angular distributions are studied. The Fresnel-type diffraction pattern is found dominant for all investigated elastic scatterings where Coulomb interaction is strong. The interaction radius of elastic scattering is found decreasing and the total cross-section increasing when the incident projectile energy increases. Moreover, the interaction radius and total reaction cross-section are found increasing with the increase in the size of target ion. Such diffractive behavior is consistent with the prescriptions of strong absorption model (SAM). Furthermore, the explanation of the diffractive features of studied elastic scattering reactions is model-independent. The Regge pole analysis reveals the existence of a pole which has its location, width, amplitude and phase angle exhibiting a common peak at energy of 24.1MeV with oscillatory behaviour at energies around this peak energy, for all elastic scattering of alpha particle on isotopes of Ni targets except that of ${}^{58}$Ni target which exhibits extra peaks for energy larger than 24.1MeV. We believe that the presence of poles is responsible for the oscillatory structure of the backward cross-sections. The variation of Regge pole parameters with both incident energy and size of target nucleus is illustrated.