Complex rotation method for the Dirac Hamiltonian

We show that the method of the complex rotation can be applied to the Dirac Hamiltonian. We compute positions and widths of resonance levels of hydrogenlike ions (with Z=1 and Z=10), described relativistically, in the presence of the uniform dc electric field (relativistic Stark effect). We show that, for small Z, positions of the resonance levels, given by the relativistic approach, agree well with known nonrelativistic results. The relativistic treatment introduces corrections on the same order both for the resonance positions and widths, and may, therefore, alter widths considerably.