  Compton scattering is one of the fundamental interaction processes of light
with matter. Already upon its discovery [1] it was described as a billiard-type
collision of a photon kicking a quasi-free electron. With decreasing photon
energy, the maximum possible momentum transfer becomes so small that the
corresponding energy falls below the binding energy of the electron. Then
ionization by Compton scattering becomes an intriguing quantum phenomenon. Here
we report a kinematically complete experiment on Compton scattering at helium
atoms below that threshold. We determine the momentum correlations of the
electron, the recoiling ion, and the scattered photon in a coincidence
experiment finding that electrons are not only emitted in the direction of the
momentum transfer, but that there is a second peak of ejection to the backward
direction. This finding links Compton scattering to processes as ionization by
ultrashort optical pulses [2], electron impact ionization [3,4], ion impact
ionization [5,6], and neutron scattering [7] where similar momentum patterns
occur.
