  From superconductors to atomic nuclei, strongly-interacting many-body systems
are ubiquitous in nature. Measuring the microscopic structure of such systems
is a formidable challenge, often met by particle knockout scattering
experiments. While such measurements are fundamental for mapping the structure
of atomic nuclei, their interpretation is often challenged by quantum
mechanical initial- and final-state interactions (ISI/FSI) of the incoming and
scattered particles. Here we overcome this fundamental limitation by measuring
the quasi-free scattering of 48 GeV/c 12C ions from hydrogen. The distribution
of single protons is studied by detecting two protons at large angles in
coincidence with an intact 11B nucleus. The 11B detection is shown to select
the transparent part of the reaction and exclude the otherwise large ISI/FSI
that would break the 11B apart. By further detecting residual 10B and 10Be
nuclei, we also identified short-range correlated (SRC) nucleon-nucleon pairs,
and provide direct experimental evidence for the separation of the pair
wave-function from that of the residual many-body nuclear system. All measured
reactions are well described by theoretical calculations that do not contain
ISI/FSI distortions. Our results thus showcase a new ability to study the
short-distance structure of short-lived radioactive atomic nuclei at the
forthcoming FAIR and FRIB facilities. These studies will be pivotal for
developing a ground-breaking microscopic understanding of the structure and
properties of nuclei far from stability and the formation of visible matter in
the universe.
