Fully relativistic time-dependent close-coupling method for electron-impact ionization of atomic ions

A fully relativistic time-dependent close-coupling method is developed based on Dirac's covariant formulation of quantum mechanics. The expansion of a one-electron wave function in spin-orbit eigenfunctions yields the well-known coupled Dirac equations in two radial wave functions, while the expansion of a two-electron wave function in coupled spin-orbit eigenfunctions yields close-coupled Dirac equations in four radial wave functions. The time-dependent Dirac equations are solved directly using numerical methods that avoid the Fermi doubling pathology. Test calculations are carried out using the one-electron coupled equations for j=1/2 elastic potential scattering from Ne9+ at 2.00 keV and using the two-electron close-coupled equations for J=0,1 ionization of Ne9+ at 4.15 keV.