Charged particle collision and the resulting scattering effect is considered to be one of the most fundamental phenomena in atomic physics. This kind of interaction is everywhere. But despite its abundance, researchers and theorists have unsuccessfully tried for years to find a complete mathematical solution to describe three-charged-body scattering in a quantum system. Finally, though, a research team at Lawrence Berkeley Laboratory may have uncovered an answer.

Hoping to solve this, the team used the SGI/Cray T3E and IBM Blue Pacific supercomputers to obtain a complete solution to the ionization of a hydrogen atom by collision with an electron. It devised a method that allows for the calculation of a highly accurate wave function for the outgoing state of a scattered particle. This function then can be interrogated for details of the incoming state and interaction, much in the same manner an experimenter would interrogate a physical system.

Using this method, the researchers derived a graph of cross-sections of scattering electrons. This graph could then be compared for accuracy against the results of real scattering experiments.

Remarkably, when experimental data points from a recent experiment were compared to the predicted cross-sections, they matched exactly. The experimental data used in the comparison was obtained when the incoming 17.6 electron-volt electrons were scattered from the hydrogen atoms.

What did these researchers do differently from their predecessors to come up with a partial solution to the three-charged-body scattering problem? Their breakthrough came when they used a mathematical transformation of the SchrĂ¶dinger wave equation known as exterior complex scaling. This let them treat the outgoing particles not as if their wave functions extend to infinity, but instead as if they simply vanish at large distances from the nucleus.

As a result, the solution remains unchanged in regions that correspond to physical reality. Researchers were then able to compute accurate solutions of the quantum-mechanical wave function of the outgoing particles. This was based upon the angular separation and distances of two electrons that were located far away from the nucleus *(see the figure)*.

Once the wave function was calculated, it was analyzed to determine the distribution of probability densitiesâ€”a computationally intensive process known as quantum mechanical flux. The analysis successfully uncovered all the dynamic information related to the particle interaction. It also enabled researchers to determine the probability of such things as producing electrons at specific energies, as well as directions from the ionized atom.

The research team consisted of scientists from Lawrence Berkeley Laboratory, Berkeley, Calif.; Lawrence Livermore National Laboratory, Livermore, Calif.; and the University of California at Davis. For more information on this ongoing collaborative project, check out the Lawrence Berkeley National Laboratory web site at *www.lbnl.com*.