Approximate solutions of the spin and pseudospin symmetries under coshine Yukawa tensor interaction.

The approximate solutions of the Dirac equation for spin symmetry and pseudospin symmetry are studied with a coshine Yukawa potential model via the traditional supersymmetric approach (SUSY). To remove the degeneracies in both the spin and pseudospin symmetries, a coshine Yukawa tensor potential is proposed and applied to both the spin symmetry and the pseudospin symmetry. The proposed coshine tensor potential removes the energy degenerate doublets in both the spin symmetry and pseudospin symmetry for a very small value of the tensor strength (H = 0.05). This shows that the coshine Yukawa tensor is more effective than the real Yukawa tensor. The non-relativistic limit of the spin symmetry is obtained by using certain transformations. The results obtained showed that the coshine Yukawa potential and the real Yukawa potential has the same variation with the angular momentum number but the variation of the screening parameter with the energy for the two potential models differs. However, the energy eigenvalues of the coshine Yukawa potential model, are more bounded compared to the energies of the real Yukawa potential model.