  Scattering of beams of light and matter from multi-electron atomic targets is
formulated in the position representation of quantum mechanics. This yields
expressions for the probability amplitude, a(b), for a wide variety of
processes. Here the spatial parameter b is the distance of closest approach of
incoming particles traveling on a straight line with the center of the atomic
target. The correlated probability amplitude, a(b), reduces to a relatively
simple product of single electron probability amplitudes in the widely used
independent electron approximation limit, where the correlation effects of the
Coulomb interactions between the atomic electrons disappear. As an example in
which a(b} has an explicit dependence on b}, we consider transversely finite
vortex beams of twisted photons that lack the translational invariance of
infinite plane-wave beams. Some experimental considerations and future
applications are briefly considered.
