【正文】 e 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 1keV. In Fig. 2, we observe three different structures: two minima and a ridge. Fig. 2.QDCS for ionization of H2 by impact of 1keV positrons for emission of electrons in the direction of the projectile deflection.The origin of the ridge is very well understood. It corresponds to the electron capture to the continuum (ECC) cusp discovered in ion–atom collisions three decades ago by Crooks and Rudd [8]. They measured the electron energy spectra in the forward direction and observed a cuspshape peak at exactly the projectile’s velocity. The first theoretical explanation [9] showed that it diverges in the same way as 1/k. This cusp structure was the focus of a large amount of experimental and theoretical research. Since the ECC cusp is an extrapolation across the ionization limit of capture into highly excited bound states, this same effect has to be present in positron–atom collisions. In fact, the observation of such an effect associated with positronium formation, while predicted two decades ago by Brauner and Briggs, remained a controversial issue. The reason for this dispute was that, in contrast to the case of ions, the positron outgoing velocity is not similar to that of impact, but is largely spread in angle and magnitude. Thus there is no particular velocity where to look for the cusp. And this is certainly so. If we evaluate the double differential cross section, we see that the cusp is clearly visible in ion–atom collisions, but just a very mild and spread shoulder in positron–atom collisions. Thus, to observe this structure it is necessary to increase the dimension of the cross section. For instance by considering a zero degree cut of the quadruple differential cross section in collinear geometry. Kover and Laricchia measured in 1998 the dσ/dEedΩkdΩK cross section in a collinear condition at zero degree, for the ionization of H2 molecules by 100keV 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 electron detection. Since the target recoil plays no significant role in this experimental situation, the present general theory gives results similar to those obtained by Berakdar [11], and both closely follow the experimental values. The same kind of experiment was performed by Sarkadi and coworkers in Argon ionization by 75keV proton impact. They measured the quadruple differential ionization cross section in a collinear geometry for ion–atom collisions for the first time, and found the ECC cusp as in positron impact at large angles. In this case, we have to keep a plete account of the kinematics in order to reproduce the experimental results [12]. 6. Thomas mechanism Let us now go back to the ionization of H2 by 1keV positron impact. A structure at 45176。 can be observed, which was predicted and explained in 1993 by Brauner and Briggs as due to the interference of two equivalent doublecollision mechanisms. Each of these processes consists of a positron–electron binary collision, followed by the deflection by 90176。 of one of the light particles by the heavy nucleus. This mechanism was proposed by Thomas [13] as the main responsible of electron capture by fast heavy ions. In this case, since the electron and positron masses are equal, these two processes interfere at 45176。. If we lower the energy from 1000eV to 100eV, this structure at 45176。 disappears, a result that is consistent with the idea that the Thomas mechanism is a high energy effect. But there is another structure, at about 176。, that persists. We will consider this structure in the next section. 7. Saddlepoint mechanism The origin of the structure at about 176。 is certainly more difficult to identify. To our best knowledge, it has not been predicted before in positron–atom collisions, even though the mechanism responsible of its origin was already been proposed in ion–atom collisions almost two decades before. The idea was that an electron could emerge from an ion–atom collision by lying in the saddlepoint of the projectile and the residual targetion potentials. This mechanism is clearly related to one of the equilibrium points discovered by Lagrange in 1772, or to the mechanism proposed by Wannier for lowenergy electron emission. In the case of ion–atom collisions, the search for theoretical and experimental evidence of this mechanism was overcast by vivid controversy [14], [15], [16], [17] and [18]. In the case of positron–atom collisions, for the electrons to be trapped in the saddle of the positron and residualion potentials, the electron and the positron must first perform a binary collision so as to end up with the right velocities(2)where εi is the binding energy of the target in the initial state. Application of energy and momentum conservation principles shows that the positron is deviated in an angle(3)Finally, for the electron to emerge in the same direction as the positron, it must suffer a subsequent collision with the residualnucleus in a Thomaslike process. In this second collision, the electron is deflected by 90176。 and the residual target ion recoils in a direction that forms an angle of about 135176。 with the electron and the positron. This mechanism is depicted in Fig. 4. Thus, to check that the proposal of a saddlepoint is correct, we look at whether our calculations show structures that are consistent with