High-precision inverse potentials for neutron-proton scattering using piece-wise smooth Morse functions*

The aim of this study is to construct inverse potentials for various ℓ -channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference. The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5 th order Runge-kutta method. We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input. Leveraging a machine learning-based genetic algorithm, we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts. Our approach yields inverse potentials for both single and multi-channel scattering, achieving convergence to a mean-squared error . The resulting scattering lengths " " and effective ranges " r" for and states, expressed as [ , r ], are found to be [5.445(5.424), 1.770(1.760)] and [–23.741(–23.749), 2.63(2.81)] , respectively; these values are in excellent agreement with experimental ones. Furthermore, the calculated total scattering cross-sections are highly consistent with their experimental counterparts, having a percentage error of less than 1%. This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.