The PESCADO Method for Autonomous Systems: An Application to Photoionization at Near-optical Wavelengths

In a recent publication, Dalen, and Selst{\o}, Phys. Rev. A {\bf 111}, 033116 (2025), it was demonstrated how converged photo electron spectra could be determined using a complex absorbing potential on a truncated numerical domain considerably smaller than the extension of the dynamical wave function. That approach required simulation until virtually all unbound parts of the wave function was absorbed, far beyond the duration of the interaction with the external field. In this work we formulate the method in a semi-analytical manner which allows us to extrapolate to infinite times after the interaction with the external field. In addition to obtaining photoelectron spectra for hydrogen differential in energy and ejection angle, we also demonstrate how -- and when -- the absorber may be seen as a detector, distorting the angular distributions when the detector is placed in the extreme vicinity of the atom.