Spin-Orbit Coupling and Relativistic Correction in Strong-Field Ionization

Spin is commonly ignored in strong-field physics. This is due to the fact that it has only been shown to play a role through spin-orbit coupling for states with high orbital-angular momentum, and with an elliptically polarized fields. Furthermore, in experiment, spin-resolved measurements have only fairly recently become possible. Thus, theoretical models treat spin only through coupling to initial states and generally neglect the spin dynamics. However, the trend for longer wavelengths, e.g. in imaging processes such as laser induced electron diffraction (LIED), means that spin dynamics may play an important role for linear fields, through high energy rescattering.

We explore spin, spin-orbit coupling, and relativistic corrections to the kinetic energy by modifying the path-integral model, the Coulomb quantum-orbit strong-field approximation (CQSFA). Spin is included into the path-integral formalism and solved exactly, while the remaining system is solved via the semi-classical saddle point method. We confirm the validity of the CQSFA method by comparing the non-relativistic model without spin-orbit coupling to a non-relativistic TDSE code, with exceptional agreement. At 1600 nm wavelengths, there are differences in the photoelectron momentum distributions when comparing with and without spin-orbit coupling or relativistic corrections. These are most apparent in the high-energy region of the photoelectron momentum distributions and are due to rescattered electron wave packets. We demonstrate that these recolliding electrons undergo a very large momentum transfer, which warrants a relativistic treatment, and leads to large spin-orbit coupling. The inclusion of these effects has an impact on both the phase and amplitude of these recolliding electronic wave packets.

The inclusion of spin-orbit coupling and relativistic correction in the CQSFA, is a key step in the accurate modelling of strong-field ionization at longer wavelengths. This work highlights effects that may have an important impact on imaging processes such as LIED or photoelectron holography, and could lead to more accurate molecular imaging.