Relativistic ionization dynamics of hydrogenlike ions in strong electromagnetic fields: Generalized pseudospectral method for the time-dependent Dirac equation

We perform a theoretical and computational study of relativistic hydrogenlike ions subject to linearly polarized strong electromagnetic fields. The time-dependent Dirac equation is solved with the help of the generalized pseudospectral method in spherical coordinates. When solving the Dirac equation numerically with basis-set methods, spurious eigenstates usually show up. We suggest a simple transformation of the original discretized Dirac Hamiltonian that removes such states and keeps highly accurate true eigenstates. We calculate the ionization probabilities of the hydrogen atom and hydrogenlike ions ${\mathrm{Ne}}^{9+}$ and ${\mathrm{Ar}}^{17+}$ for various peak field strengths and pulse durations scaled with respect to the nuclear charge of the target. Calculations are performed both within and beyond the dipole approximation. We analyze the nondipole effects and find the region of the Lorentz deflection parameter where the dipole approximation is still applicable.