Two-Nucleon Scattering without partial waves using a momentum space Argonne V18 interaction

TL;DR

This paper develops a momentum space approach to two-nucleon scattering using the Argonne V18 potential, avoiding partial wave decomposition, and computes scattering observables directly in operator form.

Contribution

It introduces a novel operator-based momentum space method for two-nucleon scattering that bypasses partial wave expansion, enabling direct calculation of scattering observables.

Findings

Accurately reproduces scattering observables across various energies.

Demonstrates the effectiveness of the operator expansion in momentum space.

Provides a comparison with partial wave results and experimental data.

Abstract

We test the operator form of the Fourier transform of the Argonne V18 potential by computing selected scattering observables and all Wolfenstein parameters for a variety of energies. These are compared to the GW-DAC database and to partial wave calculations. We represent the interaction and transition operators as expansions in a spin-momentum basis. In this representation the Lippmann-Schwinger equation becomes a six channel integral equation in two variables. Our calculations use different numbers of spin-momentum basis elements to represent the on- and off-shell transition operators. This is because different numbers of independent spin-momentum basis elements are required to expand the on- and off-shell transition operators. The choice of on and off-shell spin-momentum basis elements is made so that the coefficients of the on-shell spin-momentum basis vectors are simply related to the corresponding off-shell coefficients.