Theory of Light Hydrogenlike Bound States: High Order Corrections Ions: High Order Corrections in Muonic and Electronic Atoms and Ions

High precision quantum electrodynamics of hydrogenlike bound states is an active field of theoretical research motivated both by the spectacular experimental progress and the intellectual challenge. Despite significant progress in the theory of light hydrogenlike bound states there is 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 of this project. Improvement of the theory of the Lamb shift in muonic hydrogen and deuterium, and in light muonic helium ions is planned. Other objectives include calculation of polarizability contributions to the Lamb shift and hyperfine splitting in muonic atoms and ions, and of other unknown corrections in muonic atoms. Further development and improvement of the theory of hyperfine splitting in muonium and the theory of the Lamb shift in electronic hydrogen are among the goals of this project. 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, and 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, 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.