Theoretical developments in (e,2e) studies of excited states and in (e,3e) spectroscopy

The theory of single and double ionization of atoms deals with one of the most difficult problems in quantum mechanics: the scattering of a few charged particles. A large number of different (e,2e) experiments and theoretical calculations have helped us to understand the main physical mechanisms and their effect on the shape of triple differential cross section (TDCS). Recently the first deeply asymmetric (e,2e) experiments, leaving the residual ion in an excited state (which we indicate in this paper by (e,2e)*), and (e,3e) experiments have been performed. These offer new challenges to the theory. A very preliminary survey of main theoretical methods currently used to explain the experimental measurements is presented here. It will be shown that small differences in the choice of initial and final state models employed by different authors lead to large effects in both the shape and absolute size of the TDCS in the case of excitation ionization, even if these models give almost identical results for the (e,2e) case. A few physical mechanisms contributing to the (e,2e)* process are discussed in this paper. Special attention is given to the multichannel close-coupling method. (e,3e) experiments allow us to study the final state wave function with two continuum electrons. We obtain two unexpected results. First, we found that the two-step mechanism contribution is comparable and even bigger than that of shake-off. Second, the algorithms exploiting the angular decompositions of many-body continuum wave functions do not work in the case of long-range potentials; this is a result of the failure of the widely used diagonalization approximations in this case. The physical considerations that support these and other results are presented in this paper.