Double Ionization Dynamics Studied with Four-Body Dalitz Plots

The dynamics of double ionization (DI) of helium by ion impact has attracted widespread interest in the last decades, in particular, as electron-electron correlation effects play a much more important role than in single ionization (SI). Kinematically complete studies of DI, i.e. experiments recording the full momentum vectors of all involved particles, are very demanding due to the relatively small cross sections and the high-dimensional final momentum space. In order to obtain results with satisfying statistical quality, many events need to be collected and long measuring periods were required in earlier experimental runs. Here we report on a study of double ionization with the TSR in-ring Reaction Microscope at MPIK, which was earlier operated at the ESR [1]. Due to the high luminosity achievable in storage rings, data could be obtained in a short time for projectile ions ranging from 6MeV protons to 158 MeV Au (c.f. [2]). Fully differential cross sections (FDCS) extracted from such measurements provide the most sensitive test for theory. However, they have the drawback that they typically cover only a tiny fraction of the total cross section and thus elucidate the collision dynamics only for very specific kinematical conditions. Recently, we demonstrated that four-body Dalitz (4-D) plots are a powerful tool to present data of in double ionization [3] without loss of any part of the total cross section. By using a tetrahedral coordinate system it has become possible to present measured data as a function of all four fragments simultaneously. In Fig. 1 4-D plots are shown for double ionization of helium in collisions with 158 MeV Au. The front and bottom planes of the tetrahedron represent the ejected electrons, the backplane the He nucleus, and the right plane the projectile. The distance from a given data point to the four planes provides a set of the squared momenta of each particle normalized to the sum of these squared momenta for all four particles [3]. In the case of the projectile, the momentum transfer is used. In the upper diagrams only the transverse momentum components in the scattering plane (defined by the initial and final projectile momenta) are used. In the lower line only the longitudinal components (i.e. along the projectile beam axis) are considered. The numbers in the upper left diagram label the 6 intersection lines between adjacent tetrahedron planes. In the transversal direction (Fig. 1 a) the dominant feature is a strong maximum at intersection line 6, which is at a zero distance to the two electron planes. Thus, the electron momenta are negligible in this region and momentum is transferred predominantly between the projectile and the He nucleus. In the longitudinal direction (Fig. 1 d) binary interactions are much less important. A detailed analysis of this plot shows [2] that the “shoetongue-like” distribution is a signature of the strong postcollision interaction (PCI) between one (or both) electrons and the highly charged and relatively slow projectile ion.