Nucleon Nucleon Potential Using N$3$LO Chiral Effective Field Theory

Abstract

A microscopic description of nucleon-nucleon (NN) and nucleon-nucleus (NA) scattering is developed using chiral effective field theory (chiEFT) at next-to-next-to-next-to-leading order N3LO. The NN interaction is taken from the EGM formulation, which incorporates spectral function regularization Lambda-tilde to control short range components of the two pion exchange force, together with a Gaussian regulator Lambda to ensure convergence of the Lippmann-Schwinger (LS) equation. The regulator parameters (Lambda, Lambda-tilde) = (450, 500), (550, 600), (600, 600) MeV. The resulting chiEFT NN t-matrix is used to construct the first order optical potential, from which Wolfenstein amplitudes and elastic differential cross sections are calculated. The theoretical amplitudes (B) and (C) for pp and pn scattering at 100 and 200 MeV show good overall agreement with experimental data, with the largest discrepancies appearing in the small real component of the spin orbit amplitude. Calculations of p + 16O and p + 40Ca elastic scattering at 100 and 200 MeV reproduce the measured angular distributions with high accuracy, particularly at forward and intermediate angles. These results demonstrate that the EGM chiEFT potential provides a consistent and quantitatively reliable framework for describing NN observables and NA elastic scattering in the 100-200 MeV energy range, while highlighting the need for improved treatment of short range and spin dependent contributions at higher energies.