Elastic Differential Cross Sections for Space Radiation Applications

TL;DR

This paper compares different computational methods for calculating nuclear reaction cross sections relevant to space radiation, highlighting the advantages of the LS3D method for high-energy reactions due to its stability and convergence.

Contribution

The study evaluates and compares the eikonal, partial wave, and LS3D methods, recommending LS3D for high-energy space radiation applications due to its superior numerical stability.

Findings

LS3D method shows rapid convergence and stability for high-energy reactions.

Eikonal method is effective for light nuclei with exact optical potentials.

Partial wave method is unstable for systems requiring many partial waves.

Abstract

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann- Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A $\le$ 16), and the momentum-space representation of the optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability.