Theoretical Investigation of Low-Energy Positron and Positronium Collisions

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Vortices (or whirlpools) are familiar properties of fluids and gases and so are important in a number of fields of science and engineering, including fluid dynamics, astrophysics, condensed-matter physics and non-linear dynamics. They are examples of collective phenomena in stirred systems, and have even been observed in the ultracold atomic gases known as Bose-Einstein condensates. Surprisingly, vortices have recently been discovered in the quantum mechanical wave function describing elementary electron-atom collision processes, where their appearance was correlated to deep minima in observed scattering cross sections. The situation is still somewhat murky, since elementary collision processes seem to have little in common with the much more complex phenomena associated with the collective properties of liquids and gases. This project hopes to shed light on this mystery by searching for vortex formation in collision processes involving positrons rather than electrons. Positrons are antiparticles of electrons, carry positive charge, and so interact very differently with matter. Sensitivity to the charge of an incident projectile will therefore be tested through direct theoretical calculations, hopefully clarifying the underlying mechanism of vortex formation in these processes. Since positrons are now commonly used in a variety of fields and applications, ranging from condensed matter physics to positron-emission tomography (PET scans), the relevance of vortex formation to elementary collision processes involving positrons could have wide-ranging impact. The work will engage graduate students in challenging research projects involving elementary quantum mechanical collision processes.Recently, researchers have demonstrated that vortex formation is responsible for deep minima observed in the experimental measurements of the triply differential cross sections for electron-impact ionization of helium atoms. Vortices have also been studied for other ionization processes in atomic collisions. The first goal of this project is to analyze vortex formation in positron-hydrogen and positron-helium collisions, to see whether or not vortices affect the rate of positronium formation. The PI will guide a graduate student through a detailed analysis of positronium formation in these processes using Kohn-type variational methods, multichannel effective range theories and the Born approximation. The goal is to determine basic components necessary to obtain a zero in the positronium formation scattering amplitude, the corresponding deep minimum in the differential cross section and the vortex in the velocity field that corresponds to the scattering amplitude. A second project is to study positronium-positronium scattering, which is of interest since it is a fundamental four-body Coulomb problem, and in support of experimental efforts to make a positronium Bose-Einstein Condensate. The PI will train a graduate student to use Kohn-type variational methods and the Born approximation with exchange for this analysis. A goal is to obtain benchmark results for ground-state positronium - ground-state positronium scattering using Kohn-type variational methods.