The triply differential cross section of molecular hydrogen for ionization by 50 eV positrons has been determined, for the first time, for both the ejected electron in coincidence with the remnant ion and for the scattered projectile. Asymmetries in the energy sharing between the two light particles in the final state are observed, with the electron spectrum being shifted to significantly lower (and the scattered positron to correspondingly higher) energies than expected. A similar shape is observed in the case of the ejected electron spectrum from a helium target at the same excess energy. DOI: 10.1103/PhysRevLett.95.223202 PACS numbers: 34.85.+x The correlated dynamics of few interacting particles is a fundamental physics problem that may be exemplified through the process of ionization. Despite the tremendous progress in its theoretical description during the past decade or so (e.g., [1,2]), concomitant experimental investigations remain essential in assessing the accuracy of the various approaches and in guiding further developments. In this respect, particularly sensitive are studies in which there are two or more light particles (e.g., an electron and a positron) in the final state and which yield cross sections which are differential in the energy and/or angular distribution of the ejected electron(s) and/or scattered projectile. The most stringent among these is the triply differential cross section (TDCS) in which all the kinematic parameters are determined. A significant body of data has been gained using the (e; 2e) method (e.g., [3]) and, more recently, the COLTRIM technique (e.g., [4]), which has been applied to electron, photon, proton, and ion impact. Differential studies with positrons, mainly confined to doubly differential investigations (e.g., [5][6][7]), remain scarce but are desirable both intrinsically and for comparison with equivelocity electrons or protons to probe the role of the projectile charge or mass on the collision dynamics (e.g., [8,9]). In this Letter, we report experimental TDCS results for positron impact ionization of simple molecular and atomic targets that reveal major discrepancies with current quantum-mechanical treatments and should thus provide new insights into the understanding of three-body correlated dynamics.Over the past decade, sophisticated distorted wave calculations have been developed based on the 3-Coulombwave final-state wave function (3C) of Brauner et al. [10] which approximates the strictly inseparable many-body system in terms of pairs of interacting particles. At lower energies, the use of the eikonal approximation for the initial state has been found to improve agreement with experiments (e.g., [11]). While such methods have been successful with a variety of projectiles and over a wide energy range, nonperturbative approaches remain superior at lower energies. Particularly noteworthy in this respect are the exterior complex scaling (ECS) method (e.g., [2]), which yielded the first accurate TDCS for e ÿ -H ionization for the case of equal energy-s...