FINITE-VOLUME VARIATIONAL METHOD FOR THE DIRAC-EQUATION

A finite-volume variational principle based on the Dirac Hamiltonian is formulated in a way similar to the Kohn variational principle for the logrithmic derivative used in nonrelativistic electron-atom scattering. As in R-matrix methods, the essential idea is to solve the Dirac equation variationally within a finite reaction volume for a given total energy of the system. In contrast to previous methods, we do not need to impose any unphysical boundary conditions on the trial function. The continuation of the variational solution into the outer region is represented by a standard close-coupling expansion. The K matrix is obtained by matching the variational solutions with the solutions in the outer region on the surface enclosing the reaction volume.