Investigation of the Coupling Potential by means of S-matrix Inversion

We investigate the inelastic coupling interaction by studying its effect on the elastic scattering potential as determined by inverting the elastic scattering $S$-matrix. We first address the effect upon the real and imaginary elastic potentials of including excited states of the target nucleus. We then investigate the effect of a recently introduced novel coupling potential which has been remarkably successful in reproducing the experimental data for the $^{12}$C+$^{12}$C, $^{12}$C+$^{24}$Mg and $^{16}$O+$^{28}$Si reactions over a wide range of energies. This coupling potential has the effect of deepening the real elastic potential in the surface region, thereby explaining a common feature of many phenomenological potentials. It is suggested that one can relate this deepening to the super-deformed state of the compound nucleus, $^{24}$Mg.Comment: 12 pages with 3 figure

New Results in the Analysis of the 16^{16}O+28^{28}Si Elastic Scattering by Modifying the Optical Potential

The elastic scattering of the $^{16}$O+$^{28}$Si system has been analyzed with a modified potential within the framework of the optical model over a wide energy range in the laboratory system from 29.0 to 142.5 MeV. This system has been extensively studied over the years and a number of serious problems has remained unsolved: The explanation of the anomalous large angle scattering data; the out-of-phase problem between theoretical predictions and experimental data; the reproduction of the oscillatory structure near the Coulomb barrier; the consistent description of angular distributions together with the excitation functions data are just some of these problems. We propose the use of a modified potential method to explain these problems over this wide energy range. This new method consistently improves the agreement with the experimental data and achieves a major improvement on all the previous Optical model calculations for this system.Comment: 19 pages with 8 figure

Analytical Solutions to the Hulthen and the Morse Potentials by using the Asymptotic Iteration Method

We present the exact analytical solution of the radial Schr\"{o}dinger equation for the deformed Hulth\'{e}n and the Morse potentials within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained explicitly. Our results are in excellent agreement with the findings of the other methods.Comment: 13 pages and 2 table

A New Coupling Potential for the Scattering of Deformed Light Heavy-Ions

This letter introduces a new coupling potential to explain the experimental data over wide energy ranges for a number of systems. Within the coupled-channels formalism, this letter first shows the limitations of the standard coupled-channels theory in the case where one of the nuclei in the reaction is strongly deformed and then, demonstrates that a global solution to the problems of light heavy-ion reactions such as $^{12}$C+$^{12}$C, $^{16}$O+$^{28}$Si and $^{12}$C+$^{24}$Mg can be found using a new second-derivative coupling potential in the coupled-channels formalism. This new approach consistently improves the agreement with the experimental data for the elastic and inelastic scattering data as well as for their excitation functions using constant or slightly energy-dependent parameters.Comment: 4 Pages, 5 Figures, submitted to the Phys. Lett.

A Systematic Investigation of Light Heavy-Ion Reactions

We introduce a novel coupling potential for the scattering of deformed light heavy-ion reactions. This new approach is based on replacing the usual first-derivative coupling potential by a new, second derivative coupling potential in the coupled-channels formalism. The new approach has been successfully applied to the study of the $^{12}$C+$^{12}$C, $^{12}$C+$^{24}$Mg, $^{16}$O+$^{28}$Si and $^{16}$O+$^{24}$Mg systems and made major improvements over all the previous coupled-channels calculations for these systems. This paper also shows the limitations of the standard coupled-channels theory and presents a global solution to the problems faced in the previous theoretical accounts of these reactions.Comment: 7 pages with 4 figure

α\alpha-α\alpha Double Folding Cluster Potential Description of the 12^{12}C+24^{24}Mg System

We present a simultaneous analysis of the elastic scattering and fusion cross-section data of the $^{12}$C+$^{24}$Mg system around the Coulomb barrier and over energies by using the microscopic $\alpha$-$\alpha$ double folding cluster potential within the framework of the optical model and the coupled-channels formalism. The $\alpha$-$\alpha$ double folding cluster potential is obtained by using the $\alpha$-cluster distribution densities of the nuclei in the usual double folding procedure. The microscopic potential results are compared with the findings of the phenomenological deep and shallow potentials. It is subsequently shown that only phenomenological deep real, microscopic nucleon-nucleon and $\alpha$-$\alpha$ double folding cluster potentials provide a consistent description of the angular distributions and fusion cross-section data simultaneously. The effect of the inclusion of the excited states of the target nucleus $^{24}$Mg on the fusion cross-section predictions is also determined by the coupled-channels calculations, which are shown to improve the agreement.Comment: 4 pages Latex RevTex4 with 2 EPS Figures. Accepted for publications in Phys. Rev.