Exact Neutron-Proton Wavefunctions Using the Phase Function Method

Abstract

Radial phase shifts ($\hat{I}´(r)$), amplitude functions ($A(r)$), and exact wavefunctions ($u(r)$) for various uncoupled S, P, and D channels of neutron--proton scattering have been calculated using the Phase Function Method (PFM). In these calculations, inverse potentials obtained from the Morse function as the zeroth-order reference potential are employed. The parameters of the Morse potential were optimized using the comprehensive GRANADA partial wave analysis, consisting of 6713 experimental \textit{np} phase shift data points from 1950 to 2013, by minimizing the mean square error (MSE) as a cost function. The present work provides detailed radial dependence of $\hat{I}´(r)$, $A(r)$, and $u(r)$ up to 5~fm for laboratory energies $E_{\ell \text{lab}}=[1,10,50,100,150,250,350]$~MeV. The obtained wavefunctions show excellent agreement with high-precision Nijmegen-II results, highlighting the accuracy and transparency of the PFM approach for uncoupled scattering states.