Neutron-Proton Interaction Modeled using Morse Function: Constructing Inverse Potentials Using Variational Monte-Carlo and Phase Function Method

TL;DR

This paper models neutron-proton interactions using a Morse potential and constructs inverse potentials through variational Monte-Carlo and phase function methods, achieving high accuracy in matching experimental scattering data.

Contribution

It introduces a novel approach combining Morse function modeling with VMC and PFM to derive inverse potentials for np interactions across multiple channels.

Findings

Inverse potentials match experimental data within 5% for energies up to 1050 MeV.

Successfully modeled Coulomb and non-local spin-orbit terms with high accuracy.

Obtained phase shift data for 3S1 and 1S0 channels consistent with experiments.

Abstract

Understanding neutron-proton(np) interaction has been one of the most studied problems. One way to construct model interaction has been using inversion potentials obtained from experimental scattering phase shifts(SPS). Here, we show that, inverse potentials corresponding to SPS for various l-channels of np interaction can be obtained using variational Monte-Carlo(VMC) technique in tandem with phase function method(PFM) by modeling np-interaction as a Morse function. The S-channel SPS for 3S1 and 1S0 have been obtained, with a mean percentage error with respect to experimental multiple energy analysis data for lab energies up to 1050 MeV, to less than 5%. Similarly, inverse potential for 1S0 pp interaction, with Coulomb term modeled as proportional to erf(), has also been obtained to match experimental values to less than 4%. Non-local and spin-orbit terms are included to obtain inverse potentials for P and D channels and results match with available data to a good extent.