Solution of the time-dependent Dirac equation for describing multiphoton   ionization of highly-charged hydrogenlike ions
  A theoretical study of the intense-field multiphoton ionization of hydrogenlike systems is performed by solving the time-dependent Dirac equation within the dipole approximation. It is shown that the velocity-gauge results agree to the ones in length gauge only if the negative-energy states are included in the time propagation. On the other hand, for the considered laser parameters, no significant difference is found in length gauge if the negative-energy states are included or not. Within the adopted dipole approximation the main relativistic effect is the shift of the ionization potential. A simple scaling procedure is proposed to account for this effect. 
Yulian V. Vanne, Alejandro Saenz
quant-ph physics.atom-ph