Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.