Intermediate-state Coulomb-corrected strong-field approximation for rescattering processes
We analytically derive the all-order strong-field S-matrix series incorporating intermediate-state Coulomb-Volkov corrections (ICSFA). Focusing on rescattering processes described by the second-order term, we systematically investigate the impact of intermediate-state Coulomb interactions on above-threshold ionization (ATI) spectra of atomic hydrogen in linearly polarized laser fields. Crucially, ICSFA spectra demonstrate superior agreement with the results obtained by numerically solving the time-dependent Schr\"{o}dinger equation compared to the standard strong-field approximation (SFA) and final-state Coulomb-corrected SFA (FCSFA). Our analysis reveals that intermediate-state Coulomb corrections enhance the yield of the third- and fourth-return-recollision trajectories while modifying interference patterns in the energy spectrum. The observed enhancement of the multi-return-recollision trajectories can be attributed to modifications of the ionization yield and scattering cross-section, which are induced by intermediate-state Coulomb effects. These effects are equivalent to the so-called Coulomb focusing effect.