  In quantum physics, the theoretical study of unbound many-body systems is
typically quite complex -- owing to the combination of their large spatial
extension and the so-called {\it curse of dimensionality}. Often, such systems
are studied on truncated numerical domains -- at the cost of losing
information. Here we present methods for calculating differential probabilities
for unbound particles which are subjected to a {\it complex absorbing
potential}. In addition to attenuating outgoing waves, this absorber is also
used to probe them by projection onto single-particle scattering states, thus
rendering the calculation of multi-particle scattering states superfluous.
Within formalism based on the Lindblad equation, singly differential spectra
from subsequent absorptions are obtained by resolving the dynamics of the
remaining particles after the first absorption. While the framework generalizes
naturally to any number of particles, explicit, compact and intuitive
expressions for the differential probability distributions are derived for the
two-particle case. The applicability of the method is illustrated by numerical
examples involving two-particle model-systems. These examples, which address
scattering and photo ionization, demonstrate how energy distributions of
unbound particles may be determined on numerical domains considerably smaller
than the actual extension of the system.
