Recent experiments on double photoionization of H$_2$ with photon energies between 160 and 240 eV have revealed body-frame angular distributions that suggest classical two-slit interference effects may be present when one electron carries most of the available energy and the second electron is not observed. We report precise quantum mechanical calculations that reproduce the experimental findings. They reveal that the interpretation in terms of classical diffraction is only appropriate at substantially higher photon energies. At the energies considered in the experiment we offer an alternative explanation based on the mixing of two non-diffractive contributions by circularly polarized light.

Triple differential cross sections (TDCS) for two-photon double ionization of helium are calculated using the method of exterior complex scaling both above and below the threshold for sequential ionization (54.4 eV). It is found that sequential ionization produces characteristic behavior in the TDCS that identifies that process when it is in competition with nonsequential ionization. Moreover we see the signature in the TDCS and nuclear recoil cross sections of "virtual sequential ionization" below the threshold for the sequential process.

Excitation of the autoionizing states of helium by electron impact isshown in calculations in the s-wave limit to leave a clear signature in the singly differential cross section for the (e,2e) process. It is suggested that such behavior should be seen generally in (e,2e) experiments on atoms that measure the single differential cross section.

Above 54.4 eV, two-photon double ionization of helium is dominated by a sequential absorption process, producing characteristic behavior in the single and triple differential cross sections. We show that the signature of this process is visible in the nuclear recoil cross section, integrated over all energy sharings of the ejected electrons, even below the threshold for the sequential process. Since nuclear recoil momentum imaging does not require coincident photoelectron measurement, the predicted images present a viable target for future experiments with new short-pulse VUV and soft X-ray sources.

Electron-impact excitation and ionization of helium is studied in the S-wave model. The problem is treated in full dimensionality using a time-dependent formulation of the exterior complex scaling method that does not involve the solution of large linear systems of equations. We discuss the steps that must be taken to compute stable ionization amplitudes. We present total excitation, total ionization and single differential cross sections from the ground and n=2 excited states and compare our results with those obtained by others using a frozen-core model.

We present converged, completely ab initio calculations of the triple differential cross sections for double photoionization of aligned H2 molecules for a photon energy of 75.0 eV. The method of exterior complex scaling, implemented with both the discrete variable representation and B-splines, is used to solve the Schroedinger equation for a correlated continuum wave function corresponding to a single photon having been absorbed by a correlated initial state. Results for a fixed internuclear distance are compared with recent experiments and show that integration over experimental angular and energy resolutions is necessary to produce good qualitative agreement, but does not eliminate some discrepancies. Limitations of current experimental resolution are shown to sometimes obscure interesting details of the cross section.

Exterior complex scaling provides a practical path for first-principles studies of atomic and molecular ionization problems since it avoids explicit enforcement of asymptotic boundary conditions for 3-body Coulomb breakup. We have used the method of exterior complex scaling, implemented with both the discrete variable representation and B-splines, to obtain the first-order wave function for molecular hydrogen corresponding to a single photon having been absorbed by a correlated initial state. These wave functions are used to construct converged triple differential cross sections for double photoionization of aligned H2 molecules.