An implementation of a variational R-matrix method for the Dirac equation.

This study introduces the adaptation of the eigenchannel R-matrix method to the Dirac equation. While implementations of the R-matrix method for the Dirac equation exist, none have utilized the eigenchannel framework, known for its high effectiveness and efficiency in the non-relativistic case. Our study aims to conduct a thorough theoretical analysis of the necessary modifications required to adapt the method to the relativistic equation. We also present a detailed analysis of Coulomb-specific generalized multichannel quantum defect theory parameters in the relativistic theory. This analysis allowed us to define a convenient basis of radial functions, enabling numerical analysis with a behavior similar to non-relativistic functions. We delve into the explicit form of these functions, a detail we found overlooked in the literature. Numerical explorations on the radium atom, treated as a two-electron problem using fitted potentials, were conducted. We studied photoionization cross sections and autoionization resonances, comparing them with non-relativistic effects. Additionally, we anticipate a comparison with novel measurements of the radium spectrum. Our ultimate goal is to utilize this method for future studies on the ionization of highly stripped ions.