A joint analysis of the elastic-scattering angular distributions and fusion cross sections together with the S factor for the 16 O + 16 O system near and below the Coulomb barrier is reported. To describe these observables within the framework of the optical model, a comparative study of microscopic α-α double-folding clusters and phenomenological shallow potentials with surface-transparent imaginary parts is performed. Although the phenomenological Woods-Saxon type of shallow real potentials is unable to provide a consistent explanation of these data, the α-α double-folding cluster potential obtained by considering the α-cluster structure of 16 O provides a considerable improvement. The α-α double-folding cluster potential also reproduces the normalized resonant energy states of 32 S for the N = 24 cluster band.

A simple exact analytical solution of the relativistic Duffin-Kemmer-Petiau equation within the framework of the asymptotic iteration method is presented. Exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the Coulomb potentials. As a non-trivial example, the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method.

We apply the asymptotic iteration method to solve the radial Schrödinger equation for the Yukawa type potentials. The solution of the radial Schrödinger equation by using different approaches requires tedious and cumbersome calculations; however, we present that it is possible to obtain the bound state energy eigenvalues for any n and values easily within the framework of this method. We also show the perturbed application of this method for the same potential. Our results are in excellent agreement with the findings of the SUSY perturbation, 1/N expansion and numerical methods.

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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 α-α double folding cluster potential within the framework of the optical model and the coupled-channels formalism. The α-α double folding cluster potential is obtained by using the α-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 α-α 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.Determining the shape of the nuclear potential between two colliding pairs is a long-standing problem. Theoretical investigations of the precisely measured experimental data at high energies well over the Coulomb barrier for systems like 12 C + 12 C and 16 O + 16 O have led to the determination of the gross features of the local optical potentials. Subsequently, ambiguities have been clarified in many cases regarding the depths of the real parts of the nuclear potentials [1]. However, it is not yet possible to claim the same conclusive arguments for the shape of the nuclear potential for the reactions around the Coulomb barrier. The theoretical analysis suffers from a number of serious drawbacks such as the failure to determine the shape of the interaction potential, the reproduction of the oscillatory structure, and the out-of-phase problem between theoretical predictions and experimental data.In this context, the 12 C + 24 Mg reaction [2-6] has been extensively investigated both experimentally and theoretically. The conventional optical model analysis conducted so far fails to explain all or some of the experimental data by using shallow or deep optical potentials [2][3][4]. Moreover, there has been no detailed microscopic study using folding models that attempts to explain the individual angular distributions and fusion cross-sections data simultaneously. Therefore, we aim to analyze the 12 C + 24 Mg system for energies from 16.0 to 24.0 MeV by using the α-α microscopic double folding cluster (DFC) potential. Our results are shown in comparison with the nucleon-nucleon double folding (NN-DF) potential and phenomenological shallow (WS S ) and deep (WS 2 D ) real potentials.In this Brief Report, we first introduce the potentials used in the optical model and coupled-channels (CC) formalism. Then the optical and CC results are shown and conclusions are drawn.To make a comparative study of this reaction, we have used four different potentials for the real part of the optical model potential: Two are mic...