Time ordering in fast double ionization

We consider the role of time ordering in the production of multiply charged ions by examining the role of time ordering in two-electron transitions su ch as double ionization of atoms in fast ion-atom and photon-atom collision s. If two or more electrons are uncorrelated in space, then transitions of these electrons evolve independently in time. If the electrons are correlat ed, then the transition of one electron can affect the time evolution of th e other electron. In the interaction picture correlation in time is carried by the part of the time-ordering operator T which is antisymmetric in time . It is this part of T that gives nonequal weight to the time ordering of t he interactions causing the electron transitions. The antisymmetric part of T is nonzero only if electron correlation is present. Thus, correlation in time between transitions of different electrons is connected to spatial el ectron correlation due to the electron-electron interaction. We also note a n invariance in the product of the time and charge symmetry of the projecti le in fast ion-atom collisions. Consequently, effects of the antisymmetric part of T may be found in regions where there are substantial contributions antisymmetric in the projectile charge, Z (e.g. Z(3) contributions) to tra nsition probabilities and cross sections, as evident in double ionization o f atoms and molecules. (C) 1999 Elsevier Science B.V.