R-matrix calculations of the deuterium-tritium fusion cross section based on precise Coulomb functions

Abstract

Due to the availability of fuel, favorable kinetics, and high output energy, the deuterium-tritium (D-T) fusion reaction is dominantly used in thermonuclear fusion. This paper presents a detailed, step-by-step theoretical calculation of the D-T fusion cross-section within the framework of the phenomenological R-matrix method. The fundamental principles of the phenomenological R-matrix method are outlined. Nuclear and Coulomb interactions are addressed by the R-matrix formalism, which classifies the configuration space into internal and external regions, respectively. Precise Coulomb functions are utilized in the calculations, essential for the accurate determination of the penetration and shift factors. Precise Coulomb functions for the D+T, ⁴He+¹²C systems have been calculated. The penetration and shift factors for the D+T system for a given angular momentum have been obtained. Two different R-matrix models with parameters from recent scientific papers are employed to calculate D-T fusion cross-sections and reaction rates, which are then compared with those obtained from the ENDF/B-VIII.0 library data. Within a crucial low-energy range (from 0 to 0.1 MeV), important for fusion technology, our results show quite good agreement with experimental data, while in a high-energy range, the obtained results are slightly underestimated due to non-resonant ⁵He levels not being taken into account. These findings indicate that the models can be used for future thermonuclear fusion applications.