Geometric scaling and momentum shaping in atomic single ionization driven by a focused Gaussian laser beam

Focal-volume averaging is usually treated as an experimental correction to a local strong-field response. Here, we show that it is an active mechanism that reshapes strong-field single ionization in focused Gaussian beams. Combining Ammosov–Delone–Krainov ionization, Gaussian intensity weighting, Coulomb-corrected semiclassical propagation, and nonparaxial field corrections, we find that local saturation is converted into continued post-saturation yield growth with the geometric scaling I03/2. The same intensity mixing enhances low-momentum photoelectrons and suppresses local intensity structures, whereas the propagation-direction momentum ⟨pz⟩ remains a sensitive probe of tight-focusing nondipole dynamics.