【正文】 keV positron impact [10]. The structure is not so sharply defined as for impact observed for heavy ions because of the convolution that accounts for the experimental window in the positron and e。dΩkQDCS for ionization of H2 by impact of 1mjZj/kj. This model was proposed by Garibotti and Miraglia [6] for ion–atom collisions, and by Brauner and Briggs six years later for positron–atom and electron–atom collisions [7]. However, in all these cases the kinematics of the problem was simplified, as discussed in the previous section, on the basis of the large asymmetry between the masses of the fragments involved. In addition, Garibotti and Miraglia neglected the matrix element of the interaction potential between the ining projectile and the target ion, and made a peaking approximation to evaluate the transition matrix element. This further approximation was removed in a paper by Berakdar et al. (1992), although they kept the mass restrictions in their ionimpact ionization analysis. 5. The electron capture to the continuum cusp Let us review some results in a collinear geometry. We choose as the two independent parameters the emitted electron momentum ponents, parallel and perpendicular to the initial direction of motion of the positron projectile. The energy of the projectile is 1VfΨf. For the Borntype initial statewhich includes the free motion of the projectile and the initial bound state Φi of the target, and the perturbation potential Vi is simply the sum of the positron–electron and positron–nucleus interactions. The transition matrix may then be deposed into two termsdepending on whether the positron interacts first with the target nucleus or the electron. In order to be consistent with our full treatment of the kinematics, it is necessary to describe the final state by means of a wavefunction that considers all the interactions on the same footing. Thus, we resort to a correlated C3 wave functionthat includes distortions for the three active interactions. The finalchannel perturbation potential for this choice of continuum wave function is [5](1)In the case of pure coulomb potentials, the distortions are given bywith νjE)ΨfVi Ψi and (HE)Ψi. 4. Theoretical model The main question that we want to address in this munication is if there are some important collision properties in positron–atom collisions, that are not observable in total, single or double differential ionization cross sections, and that therefore have not yet been discovered. In order to understand the origin of these structures, we pare the corresponding cross sections with those obtained in ion–atom collisions. To fulfill this objective it is necessary to have a full quantummechanical treatment able to deal simultaneously with ionization collisions by impact of both heavy and light projectiles that is therefore equally applicable – for instance – to ion–atom or positron–atom collisions. A theory with this characteristics will allow us to study the changes of any given feature of multipledifferential crosssections when the mass relations among the fragments vary. In particular, it would allow us to study the variation when changing between the two restricted kinematical situations. The second important point is to treat all the interactions in the final state on an equal footing. As we have just explained, in ion–atom collisions, the internuclear interaction plays practically no role in the momentum distribution of the emitted electron and has therefore not been considered in the corresponding calculation. In this work, this kind of assumption has been avoided. The cross section of interest within this framework isThe transition matrix can be alternatively written in post or prior forms aswhere the perturbation potentials are defined by (H=θ2), so as to reduce the dependence of the problem to three or two independent variables, respectively. The other option is to integrate the quadruple differential cross section over one or more variables.The former has been widely used to study electron–atom collisions, while the latter has been the main tool to characterize ion–atom and positron–atom ionization collisions. Particularly important has been the use of single particle spectroscopy, where the momentum of one of the particles is measured. 3. Single particle momentum distributions In ionization by positron impact it is feasible to study the momentum distribution of any of the involved fragments. As is shown in Fig. 1, the momentum distributions for the emitted electron and the positron present several structures. First, we can observe a threshold at high electron or positron velocities because there is a limit in the kinetic energy that any particle can absorb from the system. The second structure is a ridge set along a circle. It corresponds to a binary collision of the positron with the emitted electron, with the target nucleus playing practically no role. Finally, there is a cusp and an anticusp at zero velocity in the electron and positron momentum distributions, respectively. The first one corresponds to the excitation of the electron to a lowenergy continuum state of the target. The second is a depletion due to the impossibility of capture of the positron by the target nucleus. These momentum distributions allow us to study the main characteristics of ionization collisions. However, we have to keep in mind that any experimental technique that analyzes only one of the particles in the finalstate can only provide a partial insight into the ionization processes. The quadruple differential cross sections might display collision properties that are washed out by integration in this kind of experiments. Fig. 1.0 and θ10) or a collinear motion (. 1. Introduction The simple ionization collision of a hydrogenic atom by the impact of a structureless particle, the “threebody problem”, is one of the oldest unsolved problems in physics.