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We investigate single photon double ionization (PDI) of helium at photon energies of 440 and 800 eV. We observe doubly charged ions with close to zero momentum corresponding to electrons emitted back-to-back with equal energy. These slow ions are the unique fingerprint of an elusive quasi-free PDI mechanism predicted by Amusia et al. nearly four decades years ago [J. Phys. B 8, 1248Phys. B 8, , (1975] . It results from the non-dipole part of the electromagnetic interaction. Our experimental data are in excellent agreement with calculations performed using the convergent close coupling and time dependent close coupling methods.

The polarizability of a molecule is an intrinsic property which is important for a large variety of problems. However, determining reliable values for these polarizabilities is not straightforward: for instance the standard sum over states formulation of the problem does not converge because of the need to include not only many excited states but also to allow for contributions from the continuum. Here a formulation of this technique is given which uses pseudostates to allow for physical and continuum states otherwise omitted from the expansion. The pseudostates are represented by even-tempered expansions of Gaussian-type orbitals at the molecular centre-of-mass. The method is tested for LiH, Li2, water and CO molecules. For LiH and CO, calculations for the polarizability of low-lying excited states are presented including that for the A 3Π state of CO, whose polarizability appears not to have been previously determined. It is suggested that the use of pseudostates provides a straightforward method of calculating static polarizabilities of molecules in both ground and excited electronic states. The extension of the method to the calculation of dynamic polarizabilities is discussed.

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We have applied a recently developed computational method to an experimental puzzle that involves a slow outgoing electron that is scattered by a high-energy Auger electron. Although the experiment seemed to be in a regime accurately described by classical mechanics, such classical calculations could not accurately model the angular distribution of the electron pair. Using the wavefunction from our calculations to generate the energy and angular distributions of the two electrons, we have compared our results to measurements performed at the Advanced Light Source. We have obtained good agreement between the experiment and our quantum results, attributing the poor classical result to the small number of angular momenta in the wavefunction. We have included predictions on how measurements depend on the Auger energy and/or the photoelectron energy.