Unified ab initio treatment of attosecond photoionization and Compton   scattering
  We present a new theoretical approach to attosecond laser-assisted photo- and Compton ionization. Attosecond x-ray absorption and scattering are described by $\hat{\mathrsfs{S}}^{(1,2)}$-matrices, which are coherent superpositions of "monochromatic" $\hat{S}^{(1,2)}$-matrices in a laser-modified Furry representation. Besides refining the existing theory of the soft x-ray photoelectron attosecond streak camera and spectral phase interferometry (ASC and ASPI), we formulate a theory of hard x-ray photoelectron and Compton ASC and ASPI. The resulting scheme has a simple structure and leads to closed-form expressions for ionization amplitudes. We investigate Compton electron interference in the separable Coulomb-Volkov continuum with both Coulomb and laser fields treated non-perturbatively. We find that at laser-field intensities below 10$^{13}$ Wcm$^{-2}$ normalized Compton lines almost coincide with the lines obtained in the laser-free regime. At higher intensities, attosecond interferences survive integration over electron momenta, and feature prominently in the Compton lines themselves. We define a regime where the electron ground-state density can be measured with controllable accuracy in an attosecond time interval. The new theory provides a firm basis for extracting photo- and Compton electron phases and atomic and molecular wavefunctions from experimental data. 
G. L. Yudin, D. I. Bondar, S. Patchkovskii, P. B. Corkum, and A. D.   Bandrauk