An area of fundamental research is the study of the energy levels of hydrogen-like atoms and exotic atoms (atoms where one particle such as an electron is replaced by another such as a muon). Experiments have become more and more accurate, testing the theory at a stronger and stronger level. This supplies a test of our understanding of the physics of these systems. This project will calculate energy levels for systems where there have been discrepancies between theory and experiment. The theoretical results obtained in this research will find applications in the analysis of the forthcoming experimental results on muonic and electronic atoms and ions. This analysis will result in more precise values of the fundamental physical constants, especially the proton radius, as well as radii of the deuteron and alpha particles. These values will find applications in metrology and nuclear physics. New theoretical expressions will be used in the new CODATA analysis of the fundamental physical constants. In its turn CODATA compilations of the fundamental constants are used in every science classroom, and in numerous fields of science and engineering, from fundamental research to consumer electronics. Graduate and undergraduate students participating in this research will acquire research, computer, problem solving, and presentation skills. Research activity of a graduate student is expected to lead to a PhD thesis. This project will promote international collaboration, as collaboration with foreign scientists is planned. The results of the proposed research will be published in refereed journals, will be presented at domestic and international conferences and workshops, and will be used in teaching graduate courses.
High precision quantum electrodynamics of hydrogenlike bound states is an active field of theoretical research, motivated both by spectacular experimental progress and the intellectual challenge. Despite significant progress in the theory of light, hydrogenlike bound states, there are a number of challenging problems in this field that are addressed in this project. Search for a theoretical explanation of the discrepancy between the value of the proton charge radius obtained from the experiment with muonic hydrogen and the proton charge radius derived from hydrogen spectroscopy and electron-proton scattering is one of the main objectives. Irrespective of the way the proton charge radius controversy will be resolved, an extensive program of research on energy splittings in light muonic atoms and ions (muonic hydrogen, muonic deuterium, and muonic helium ions) is in order to match current and forthcoming experimental results. Methods of nonrelativistic and relativistic quantum electrodynamics will be applied to loosely bound two-particle systems in the proposed research. Theoretical results of the proposed research together with the theoretical results of other authors and with the results of the past and ongoing experiments would allow the determination of more precise values for many fundamental physical constants: the proton charge radius, the Rydberg constant, electron-muon and electron-proton mass ratios, etc.
