In this article, we present the analytical solution of the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different δ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.

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.

The approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ = λ = 1, and β = 0, are investigated.

In this paper, we study the connection between the interaction and the low energy observables, in particular the cross section for He and HeX, the helium nucleus with a heavier particle attached, to explain problems with the observed lithium abundance in the big-bang nucleosynthesis. We treat the processes 4 He + 2 H → 6 Li + γ and 4 HeX − + 2 H → 6 Li + X − and primarily focus on the effects of the long-range part of the total potential on the cross section. Our results indicate that relatively small changes in the long-range part of the potential can have a profound affect. Additionally, we compare the relative impacts on the low energy cross section of the Coulomb barrier peak and the long-range part of the interaction. Our results confirm that the long-range potential dominantly influences the low energy observables.

We present an alternative and accurate solution of the radial Schrödinger equation for the Hellmann potential within the framework of the asymptotic iteration method. We show that the bound state energy eigenvalues can be obtained easily for any n and ℓ values without using any approximations required by other methods. Our results are compared with the findings of other methods.