An approximate evaluation procedure is derived for a second-order theo
ry of coupled nucleon transport in one dimension. An analytical soluti
on with a simplified interaction model is used to determine quadrature
parameters to minimize truncation error. Effects of the improved meth
od on transport solutions with the BRYNTRN data base are evaluated. Co
mparisons with Monte Carlo benchmarks are given. Using different shiel
d materials, the computational procedure is used to study the physics
of space protons. A transition effect occurs in tissue near the shield
interface and is most important in shields of high atomic number.