Collisional Breakup in a Quantum System of Three Charged Particles

Since the invention of quantum mechanics, even the simplest example of the collisional breakup of a system of charged particles, e − + H → H + + e − + e − (where e − is an electron and H is hydrogen), has resisted solution and is now one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculation of the energies and directions for a final state in which all three particles are moving away from each other. Even with supercomputers, the correct mathematical description of this state has proved difficult to apply. A framework for solving ionization problems in many areas of chemistry and physics is finally provided by a mathematical transformation of the Schrödinger equation that makes the final state tractable, providing the key to a numerical solution of this problem that reveals its full dynamics.