Kapur-Peierls and Wigner R-matrix theories for the Dirac equation

An R-matrix theory for the Dirac equation is shown to exist in spite of incompleteness of a relativistic R-matrix basis on the reaction surface, a phenomenon which does not occur in the non-relativistic case. The theory is constructed for the most general boundary conditions imposed on expansion basis functions. It is shown that the incompleteness of the expansion basis on the reaction surface results in a matrix correction appearing in the eigenfunction expansion of the R-matrix. The correction vanishes in the on-relativistic limit. The approach is applied to the relativistic generalization of the Kapur-Peierls and Wigner resonance reaction theories. author)