ACCURATE SPLINE SOLUTIONS OF THE RADIAL DIRAC-EQUATION

The spline-Galerkin method has been applied to the solution of the Dirac equation for the bound states of hydrogenlike systems. A universal grid based on the transformation rho = r1/4 of the independent variable is shown to be preferable to the more commonly adopted transformation rho p=log r. With this universal grid, accuracies of 10-14 digits can readily be achieved for Z<100 with splines of order eight. A similar grid, modified inside the nuclear volume and in the vicinity of the nuclear ''skin'', has been used successfully in conjunction with a Fermi distribution of charge.