On the solution of the time dependent Dirac equation for hydrogen-like systems

Full text: The time dependent Dirac equation for a hydrogen-like system exposed to a short, intense electromagnetic pulse is solved numerically by expanding the wave function in eigenstates of the unperturbed Hamiltonian. These eigenstates are obtained by diagonalizing the Dirac Hamiltonian on an exponential grid. As the field parameters (field strength and frequency) increase, both magnetic and relativistic effects become important. Furthermore, for higher nuclear charges, relativistic effects are important even for relatively weak fields. The need for a non-dipole and relativistic treatments is investigated by direct comparison with the corresponding predictions of the Schroedinger equation in the dipole approximation. Although the fields considered are far below the threshold for pair-creation, negative energy states may still play a role during the interaction. The possible influence of such states is considered by propagating the wave function in field dressed states, which are obtained by diagonalizing the full Hamiltonian. After each diagonalization the negative energy states are removed from the basis. In order to minimize the number of basis states needed, complex scaling has been applied. (author)