A New Approach for Parameters of Nucleon-Nucleon Scattering at Low Energies in One and Two Dimensions

Many of the important properties of multi-nucleon systems can be found by studying the nucleon- nucleon interactions. In this work, a suitable central and an appropriate noncentral potential have been used to study nucleon- nucleon scattering in one and two dimensions. The phase shift, scattering cross section, length and amplitude are calculated using the Nikiforov-Uvarov (NU) method and WKB approximation. Comparison between the results of the suggested model in this article and the experimental reported values indicates that there is a good consistency between them.

Path integral treatment of a noncentral electric potential

We present a rigorous path integral treatment of a dynamical system in the axially symmetric potential $V(r,\theta ) = V(r) + \tfrac{1} {{r^2 }}V(\theta ) $ . It is shown that the Green’s function can be calculated in spherical coordinate system for $V(\theta ) = \frac{{\hbar ^2 }} {{2\mu }}\frac{{\gamma + \beta \sin ^2 \theta + \alpha \sin ^4 \theta }} {{\sin ^2 \theta \cos ^2 \theta }} $ . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number l ≥ 0, are recovered.