Effect of spin-orbit coupling in laser-induced ionization of atoms

Based on the expansion of the time-dependent Dirac equation in the second order on the reciprocal of the speed of light, we derive a simplified second-order time-dependent Pauli equation (second-TDPE) for single-active-electron systems, in which the time-dependent spin-orbit interaction is taken into account. A numerical method is presented for calculating the observables for atoms interacting with the electric fields of laser pulses. It is shown that the energy-level splitting between the p(+)up arrow and p(+)down arrow (as well as the p(-)up arrow and p(-)down arrow) orbitals can be reproduced by the spin-orbit coupling (SOC) term of the second-TDPE. By numerically solving the second-TDPE, we demonstrate the SOC effect in single-photon, multiphoton, and tunneling ionization of atomic Kr with valence p orbitals. In particular, a few counterintuitive strong-field ionization phenomena are discussed and analyzed. The present work provides a convenient way to explore the SOC effect in strong-field interactions.