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 o f incompleteness of a relativistic R-matrix basis on he reaction surfa ce, a phenomenon which does not occur in the non-relativistic case. Th e theory is constructed for the most general boundary conditions impos ed on expansion basis functions. It is shown that the incompleteness o f the expansion basis on the reaction surface results in a matrix corr ection appearing in the eigenfunction expansion of the R-matrix. The c orrection vanishes in the non-relativistic limit. The approach is appl ied to the relativistic generalizations of the Kapur-Peierls and Wigne r resonance reaction theories.