\begin{document}$ \leq 10^{-3} $\end{document}. The resulting scattering lengths "\begin{document}$ a_0 $\end{document}" and effective ranges "r" for \begin{document}$ ^3S_1 $\end{document} and \begin{document}$ ^1S_0 $\end{document} states, expressed as [\begin{document}$ a_0 $\end{document}, r], are found to be [5.445(5.424), 1.770(1.760)] \begin{document}$\rm fm$\end{document} and [–23.741(–23.749), 2.63(2.81)] \begin{document}$\rm fm$\end{document}, 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."> High-precision inverse potentials for neutron-proton scattering using piece-wise smooth Morse functions -
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