New Technique Shows Promise for Analysis of Three-Body Collision Problems
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MRS BULLETIN/MARCH 2000
These infinities make it impossible to define the final state of scattering exactly. “The form of the wave function where all three particles are widely separated is so intractable that no computer-aided numerical approach has been able to incorporate it explicitly.” Previously, however, in the Proceedings of the Royal Society, Colm T. Whelan of the University of Cambridge and his colleagues published their conclusion that all such approximations perform inconsistently and that those few cases which appear to yield good agreement with
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For over half a century, theorists have tried to provide a complete solution to scattering in a quantum system of three charged particles, one of the most fundamental phenomena in atomic physics. Collaborators at Lawrence Berkeley National Laboratory, Lawrence Livermore National Laboratory, and the University of California—Davis have used supercomputers to obtain a complete solution of the ionization of a hydrogen atom by collision with an electron. As reported in the December 24, 1999, issue of Science, the researchers employ 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 vanish at large distances from the nucleus. Bill McCurdy, Berkeley Lab’s Associate Laboratory Director for Computing Sciences and a principal author said, “Using this transformation, we compute accurate solutions of the quantummechanical wave function of the outgoing particles, and from these solutions, we extract all the dynamical information of the interaction.” McCurdy and his team begin with a transformation of the Schrödinger equation called “exterior complex scaling,” invented by Barry Simon of the California Institute of Technology in 1979 to prove formal theorems in scattering theory. The transformation leaves the solution unchanged in regions that correspond to physical reality, producing the correct outgoing waveform based upon the angular separation and distances of two electrons far from the nucleus. Once the wave function has been calculated, it must be analyzed by computing the “quantum mechanical flux,” a means of finding the distribution of probability densities that dates from the 1920s. This computationally in
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