Probing Wigner Time Delays with Photoelectron Interferometry: Anisotropic Long-Range Imprint of the Short-Range Centrifugal Potential

We consider the comparative dynamics of one- and two-photon ionization in atoms through semianalytical representations of the continuum wave functions, in order to model the probe-induced anisotropy in interferometric measurements of photoemission delays. We find an approximate expression of the long-range half-scattering phase based on an asymptotic expansion of the continuum eigenfunctions within the Wentzel-KramersBrillouin approximation, which encompasses and expands commonly used lower-order derivations. Combined with a perturbative approach, the resulting analytic formalism can treat, at the same time, the two-photon propensity rules, the anisotropy in the continuum-continuum photoionization time delay, and the soft-photon regime.