The fully differential cross section for the positron-and electron-impact ionization of H 2 is calculated. For positron impact the results are contrasted against a recent experiment which evidently shows the influence of the electron capture to a low-lying positronium continuum state. From a detailed analysis it is deduced that the capture probability is dependent on the orientation of the electron-positron relative momentum vector with respect to the residual ion. Within the used model, this asymmetric positronium formation is traced back to the distortion of the positron motion by the two-center potential formed by the residual ion and the secondary electron. [S0031-9007(98)06857-4] A detailed understanding of correlated many-body scattering states is of fundamental importance for diverse fields of physics such as discharge and plasma physics, fusion physics, and physics of the upper atmosphere. Such continuum states are usually achieved as the final outcome of charged particle-and photon-impact ionization. Recent technological advances in multiple detection techniques have rendered possible an unprecedented insight into the properties of these states: the energy and momentum transfer to the many-body continuum can be probed independently by virtue of equivelocity heavy-and lightparticle impact; for a fixed amount of energy and momentum transferred to the final state, the open reaction channels as well as the total potential surface can be varied using particle and antiparticle projectiles.A unified description of all of these facets is a major challenge for current theoretical investigations.The present study is motivated by a recent kinematically complete experiment [1] in which a H 2 molecule is ionized upon positron impact. The resulting final continuum states which consist of a positron and an electron moving in the field of H 1 2 [hereafter referred to as ͑e 2 e 1 H 1 2 ͒] have been simultaneously resolved in angle and energy.Contrasting this final channel with that achieved in electron-impact ionization [two electrons in the double continuum of a residual ion, labeled hereafter by ͑e 2 e 2 H 1 2 ͒], two distinctive differences can be noted. (i) Evidently the total potential surface is markedly different in both cases [2] which results in completely different dynamics. This is particularly reflected by the decisively different threshold laws for total breakup (cf. [3][4][5] and references therein).(ii) The indistinguishability of the two electrons introduces exchange effects in the case of ͑e 2 e 2 H 1 2 ͒, i.e., the cross sections are statistical mixtures of triplet and singlet scattering cross sections. While this effect is absent in the case of ͑e 2 e 1 H 1 2 ͒, an additional channel opens, namely, that of positronium formation.In the experiment of Kövér and Laricchia [1], capture of the ejected electron to low-lying positronium contin-uum states can be identified. This channel shows up as a rapid increase in the cross section when the electron approaches the positron in velocity space. The function...