Theory of Light Hydrogenlike Bound States: High Order Corrections to Lamb Shift, Hyperfine Splitting, and g-Factors

University Of Kentucky Research Foundation, Lexington KY

Investigators

Abstract

Recent years witnessed a steady progress in the field of high precision quantum electrodynamics of hydrogenlike bound states. Both the experimental errors and the accuracy of theory were signifcantly improved. As often happens this rapid progress leads to new problems. In the field of high precision quantum electrodynamic theory of bound states the long term problems are as follows; 1. The theoretical error of the 1S Lamb shift in hydrogen should be reduced signifcantly below the level of 1 kHz (and respectively of the 2S Lamb shift significantly below tenth of kHz) 2. The theoretical error of the hyperfine splitting in muonium should be reduced to about 10 Hz 3. The theoretical error of the 2S-2P Lamb shift in muonic hydrogen should be reduced below .001meV. All main theoretical problems of the theory of light hydrogenlike atomes will be addressed in the proposed research. Its main objectives include; 1. Complete calculation of all three loop nonrecoil corrections of order \alpha^3(Z \alpha)^5m to the Lamb shift in hydrogen. These are the largest still unknown contributions to the Lamb shift. Respective three loop nonrecoil corrections to hyperfine splitting in hydrogen and muonium also will be calculated. 2. Complete calculation of all three loop radiative recoil corrections of order \alpha^3(m/M) E_F to hyperfine splitting in muonium. 3. Calculation of nonlogarithmic corrections of order \alpha^2(Z \alpha)^4 m to the Lamb shift in muonic. Calculation of light by light electron loop contribution of order \alpha^2(Z \alpha)^3 m to the Lamb shift in muonic hydrogen. 4.Resolution of the discrepancy in the theory of bound state g factors in systems including particles with spins j \neq 1/2/