Exact Neutron-Proton Wavefunctions Using the Phase Function Method

TL;DR

This paper employs the Phase Function Method to compute exact neutron-proton wavefunctions and phase shifts, using optimized inverse Morse potentials fitted to extensive experimental data, achieving high accuracy in scattering state calculations.

Contribution

It introduces a detailed application of the Phase Function Method with inverse Morse potentials to accurately compute neutron-proton wavefunctions across multiple energies, validated against high-precision data.

Findings

Wavefunctions agree with Nijmegen-II results

Radial dependence of phase shifts and amplitudes detailed up to 5 fm

Method achieves high accuracy in uncoupled scattering states

Abstract

Radial phase shifts ($\delta(r)$), 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 $\delta(r)$, $A(r)$, 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.