RUI: Calculation of Higher Order Corrections to Positronium Energy Levels

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Positronium is the bound system consisting of the electron and its antiparticle, the positron. As such, it forms an “exotic atom”, similar in many ways to traditional simple atoms such as hydrogen and helium, but different because of its unique composition and because of its tendency to annihilate, transforming into pure electromagnetic energy in the form of high-energy photons. Many properties of positronium, such as energy levels and lifetimes, are accessible to high-precision experiments. Positronium properties can also be calculated theoretically to high precision using the methods of bound-state Quantum Electrodynamics (QED) because strong and weak interaction effects are negligible. Consequently, positronium is an ideal system for testing the limits of QED bound state physics and for exploring the consequences of agreement or disagreement between theory and experiment at this high level of precision. The activities involved in calculating the positronium energy levels will be of great educational value to the undergraduate students at Franklin & Marshall College involved as collaborators in that work. The students will learn theoretical methods and techniques of calculation more advanced than those usually encountered at the undergraduate level. They will gain valuable experience by doing the research, by presenting their results at professional meetings, and by publishing their work as co-authors in research journals. Positronium energy levels of low-lying states (n=1 and n=2) have been measured with uncertainties of roughly 1 MHz, and experiments are presently being developed and performed to significantly reduce some of these uncertainties. The 1S-2S transition is of particular interest because it has the smallest natural line-width and thus the greatest potential for improvement. These transition energies and more will be calculated to a new and higher level of precision. The calculations will be based on the low-energy effective quantum field theory NRQED (Non-Relativistic QED), which provides a natural and efficient framework for the study of non-relativistic atoms such as positronium.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.