[Above] Tom Rescigno, William Isaacs, Mark Baertschy, and Bill McCurdy found the solution to the problem of the scattering of three charged particles in a quantum system.
Visualizations by Mark Baertschy of UC Davis and Terry Ligocki of the NERSC/Berkeley Lab Visualization Group graced the December 24, 1999 cover of Science. The images show a representative radial wave function of two electrons in the collision of an electron with a hydrogen atom. (©1999 by the American Association for the Advancement of Science. Used with permission.)

For over half a century, theorists have tried and failed to provide a complete solution to scattering in a quantum system of three charged particles, one of the most fundamental phenomena in atomic physics. Such interactions are everywhere; ionization by electron impact, for example, is responsible for the glow of fluorescent lights and for the ion beams that engrave silicon chips.

Now, a research team using NERSC's Cray T3E and the IBM Blue Pacific computer at Lawrence Livermore National Laboratory have obtained a complete solution of the ionization of a hydrogen atom by collision with an electron, the simplest nontrivial example of the problem's last unsolved component. Bill McCurdy, Berkeley Lab's Associate Laboratory Director for Computing Sciences, along with his longtime collaborator Thomas Rescigno, a staff physicist at Livermore Lab, and their co-authors, doctoral candidate Mark Baertschy of UC Davis and postdoctoral fellow William Isaacs of Berkeley Lab, reported their findings in the December 24, 1999, issue of Science magazine.

Their breakthrough employs a mathematical transformation of the Schrödinger wave equation that makes it possible to treat the outgoing particles not as if their wave functions extend to infinity-as they must be treated conventionally-but instead as if they simply vanish at large distances from the nucleus. "Using this transformation we compute accurate solutions of the quantum-mechanical wave function of the outgoing particles, and from these solutions we extract all the dynamical information of the interaction," says McCurdy.

The method developed by McCurdy and colleagues allows the calculation of a highly accurate wave function for the outgoing state that can be interrogated for details of the incoming state and interaction in the same way an experimenter would interrogate a physical system. Comparison with real scattering experiments proves the accuracy of the new method. The experimental data points match the graph of the calculated cross sections with astonishing exactitude.