Attosecond photoelectron interference in the separable Coulomb-Volkov continuum

We develop a description of laser-assisted x-ray photoionization based on a sudden approximation approach. By splitting the system evolution into three time stages we find necessary and sufficient conditions for spatial and temporal separation of Coulomb and Volkov continuum solutions. Using the separable Coulomb-Volkov wavefunction we present an analytical non-relativistic quantum theory of attosecond photoionization. It applies for arbitrary x-ray parameters, with both Coulomb continuum and laser field treated non-perturbatively. The theory provides a firm basis for characterizing photoelectron phase and atomic and molecular wavefunctions, by extracting them from experimental data. Using the molecular hydrogen ion as a test case, we display a variety of photoelectron interference sources in energy- and angular-resolved spectra for different pulse durations, chirps and delay times between x-ray pulse replicas. (fast track communication)