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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.