Study of np-scattering for S, P and D Waves using Deng-Fan Potential by Phase Function Method

In this paper, the np - scattering phase shifts and cross section for S,P and D partial waves have been obtained for energies below the pion threshold, by considering Deng-Fan potential as model of interaction. The radial time independent Schr\"odinger equation has been analytically solved using Nikiforov - Uvarov method to obtain the energy expression for ground state of np system. Utilising this, the scattering phase shifts for $^3S_1$ have been obtained using phase function method. The phase equations for various scattering states $^1S_0$, $^1P_1$, $^3P_{0,1,2}$, $^1D_2$, and $^3D_{1,2,3}$ have been numerically solved for obtaining corresponding scattering phase shifts and their respective partial cross section. The total scattering cross sections computed at various energies are found to be closely matching with experimental data. The low energy scattering parameters determined from scattering phase shifts of $^3S_1$ and $^1S_0$ are reasonably close to experimental ones. Hence, Deng-Fan potential is a good phenomenological potential to understand the np - scattering system.