## Grants and Contracts Details

### Description

Overview. The objectives and methods of the proposed research include:
Search for a theoretical explanation of the proton charge radius discrepancy. Further development
of the theory of Lamb shift and hyperne splitting in muonic hydrogen and deuterium, and in light
muonic helium ions 4He and 3He, calculation of new corrections in light muonic atoms.
Complete calculation of all three-loop radiative-recoil corrections of order 3(m=M)EF to hyper-
ne splitting in muonium.
Complete calculation of all three-loop nonrecoil corrections of order 3(Z)5m to the Lamb shift
in hydrogen. These are the largest still unknown contributions to the Lamb shift. Respective three-loop
nonrecoil corrections to hyperne splitting in hydrogen and muonium also will be calculated.
Preparation of an updated and expanded edition of the monograph M. I. Eides, H. Grotch, and
V. A. Shelyuto, Theory of Light Hydrogenic Bound States, Springer 2007.
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 to determine more precise values for many fundamental physical constants: the proton
charge radius, the Rydberg constant, electron-muon and electron-proton mass ratios, etc.
Intellectual Merit. High precision quantum electrodynamics of hydrogenlike bound states is an
active eld of theoretical research motivated both by the spectacular experimental progress and the
intellectual challenge. Light muonic atoms and ions moved recently to the forefront of theoretical re-
search after remarkable experimental results on the Lamb shift in muonic hydrogen. Despite signicant
progress in the theory of light hydrogenlike bound states there is a number of challenging long term
problems in this eld that are as follows:
Resolution 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. 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.
The theoretical error of the hyperne splitting in muonium should be reduced to about 10 Hz.
The theoretical error of the 1S Lamb shift in hydrogen should be reduced signicantly below the
level of 1 kHz (and, respectively, of the 2S Lamb shift signicantly below tenth of kHz).
These main theoretical problems of the theory of light hydrogenlike atoms and ions will be addressed
in the proposed research.
Broader Impact. The proposed research will have broader impacts, beyond the eld of theoretical
atomic physics, rst of all in theoretical particle physics. Our new results should nd applications in
the analysis of the forthcoming experimental results on muonic and electronic atoms and ions. Com-
bined with the experimental data, these results will lead to 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 nd applications in metrology and nuclear physics that are natural consumers of the
precise values of the fundamental physical constants. 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 elds of science
and engineering, from fundamental research to consumer electronics. A new edition of the monograph
mentioned above will help to disseminate the results and methods of the modern bound state theory
among a wide cross discipline audience, and will be helpful in graduate education. Both graduate
and undergraduate students will participate in this research and besides learning physics will acquire
computer and problem solving skills. Students will make presentations at the APS meetings. Research
activity of a graduate student is expected to lead to a PhD thesis. This project will promote devel-
opment of international collaboration, an active participation of a Russian theorist is planned. The
results will be published in refereed journals, will be presented at domestic and international confer-
ences and workshops, and will be used in teaching graduate courses. These results will be also reported
at multidisciplinary conferences and workshops.

Status | Finished |
---|---|

Effective start/end date | 9/1/14 → 8/31/18 |

### Funding

- National Science Foundation: $225,000.00

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