Phase Shift Analysis of Nucleon Scattering on Light Nuclei Using Phase Function Method

The neutron and proton scattering with stable alpha particles can be modeled as a two-particle system. In this paper, using the Morse function, local interaction potentials for various $\ell$-channels have been constructed directly from scattering phase shifts (SPS) data for light nucleon-nucleus systems. The phase equation for various $\ell$-channels has been numerically solved to obtain SPS. Our research employs an optimization approach encompassing parameter boundary setting, cost function formulation, and optimization routine utilization to achieve optimal model-parameter fitting with experimental data, ensuring clarity and convenience in our analysis. The resonance energies obtained(experimental) from partial cross-section plots for the $p_{1/2}$ and $p_{3/2}$ states in the $n\alpha$ system are 4.10(4$\pm$1) and 0.93(0.89) MeV, respectively, while those in the $p\alpha$ system are 5.31(5$\pm$2) and 1.97(1.96) MeV. While the total cross-section for the $n\alpha$ system matches values available in the literature, that of the $p\alpha$ system follows the correct trend.