  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.
