The phase-functions method and full cross-section of nucleon-nucleon scattering

TL;DR

This paper introduces a phase-functions method for calculating nucleon-nucleon scattering phase shifts and cross-sections, demonstrating good agreement with existing methods and potentials, thus providing a reliable computational approach.

Contribution

The paper presents a novel application of the phase-functions method to compute nucleon-nucleon scattering phase shifts and cross-sections using various realistic potentials.

Findings

Phase shifts calculated with the method agree well with existing results.

Cross-section calculations are consistent with literature.

Differences between methods are within a few percent.

Abstract

For calculation of the single-channel nucleon-nucleon scattering a phase-functions method has been considered. Using a phase-functions method the following phase shifts of a nucleon-nucleon scattering are calculated numerically: nn (1S0-, 3P0-, 3P1-, 1D2-, 3F3- state), pp (1S0-, 3P0-, 3P1-, 1D2- state) and np (1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2- state). The calculations has been performed using realistic nucleon-nucleon potentials Nijmegen groups (NijmI, NijmII, Reid93) and potential Argonne v18. Obtained phase shifts are in good agreement with the results obtained in the framework of other methods. Using the obtained phase shifts we have calculated the full cross-section. Our results are in good agreement with those obtained by using known phases published in literature. The odds between calculations depending on a computational method of phases of scattering makes: 0,2-6,3% for pp- and 0,1-5,3% for np- scatterings (NijmI, NijmII), 0,1-4,1% for pp- and 0,1-0,4% for np- scatterings (Reid93), no more than 4,5% (Argonne v18).