(a) Amplitude ratio W and (b) phase-shift difference (relative phase) Δ extracted from experimental PADs (red diamonds) and calculated from wavefunctions obtained by TDSE simulations (black bullets)
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Figure 3. (a) Amplitude ratio W and (b) phase-shift difference (relative phase) Δ extracted from experimental PADs (red diamonds) and calculated from wavefunctions obtained by TDSE simulations (black bullets). Theoretical scattering phase-shift difference Δsc  is represented by a blue solid line in panel (b).
The two-photon ionization of helium atoms by ultrashort extreme-ultraviolet free-electron laser pulses, produced by the SPring-8 Compact SASE Source test accelerator, was investigated at photon energies of 20.3, 21.3, 23.0 and 24.3 eV. The angular distribution of photoelectrons generated by two-photon ionization is obtained using a velocity map imaging spectrometer. The phase-shift differences and amplitude ratios of the outgoing s and d continuum wave packets are extracted from the photoelectron angular distributions. The obtained values of the phase-shift differences are distinct from scattering phase-shift differences when the photon energy is tuned to a resonance with an excited level or Rydberg manifold. The difference stems from the co-presence of resonant and non-resonant path contributions in the two-photon ionization by femtosecond pulses. Since the relative contribution of both paths can be controlled in principle by the pulse shape, these results illustrate a new way to tailor the continuum wave packet.