Iterative Solution Of The One-Electron Dirac Equation Based On The Bloch Equation Of The 'Direct Perturbation Theory'

The one-electron Dirac equation is solved in an iterative manner starting with the solution of the Schrodinger equation. The method is based on 'direct perturbation theory' for relativistic effects generalized to the case of a set of near-degenerate strongly interacting states. Relativistic energies are obtained by solving a Schrodinger-like equation within a non-relativistic model space. The effective hermitian Hamiltonian and symmetric metric operator are expressed with the help of a Moller waveoperator Ohm, which generates the complete four-component Dirac wavefunction from the non-relativistic two-component one. The corresponding Bloch equation is solved to infinite order by iteration in a basis of atom-centered Gaussian;type functions for the ground state of hydrogen-like ion Eka Pt109+ and for a few states of the heavy quasi-molecule Th-2(179+). (C) 1999 Elsevier Science B.V. All rights reserved.