Based on the generalized reduced R-matrix theory, the R-matrix analysis code (RAC program) was used to analyze the experimental data of all the nuclear reaction channels related to the \(^{5}\) He system. The current calculations provide accurate and reliable evaluation data and are in good agreement with the experimental data. In this study, self-consistent evaluation data for each reaction were obtained using multi-channel and multi-energy fitting. In particular, the error propagation theory of generalized least squares was used to determine the error of the evaluation data and the covariance matrix of the integral cross section. This R-matrix analysis for the \(^{5}\) He system has three features. First, for the first time, the error in the evaluation data of the T(d,n) \(^{4}\) He reaction cross section and the covariance matrix of the integral cross section are provided. Second, we used only one set of R-matrix parameters to depict the reaction cross section of each reaction channel of the \(^{5}\) He system for the entire energy region in our work. Third, in this evaluation, we considered some of the latest measured experimental data, especially after 2000. The T(d,n) \(^{4}\) He reaction cross section at 0.1 MeV and below was carefully studied. The effect of different energy levels in T(d,n) \(^{4}\) He was analyzed, with the energy levels 3/2 \(^{+}\) making a major contribution to the cross section, and the role of the S-wave and P-wave from 3/2 \(^{-}\) determines the lean forward trend of the angular distributions at 0.01–0.1 MeV.
