Irreducible Three-loop Vacuum-polarization Correction In Muonic Bound Systems

Three-loop electronic vacuum-polarization corrections due to irreducible diagrams are evaluated for two-body muonic ions with nuclear charge numbers 1≤Z≤6. The corrections are of order α3(Zα)2mr, where α is the fine-structure constant and mr is the reduced mass. Numerically, the energy corrections are found to be of the same order of magnitude as the largest of the order α2(Zα)6mr corrections, and are thus phenomenologically interesting. Our method of calculation eliminates numerical uncertainty encountered in other approaches

Access to improve the muon mass and magnetic moment anomaly via the bound-muon gg factor

A theoretical description of the $g$ factor of a muon bound in a nuclear potential is presented. One-loop self-energy and multi-loop vacuum polarization corrections are calculated, taking into account the interaction with the binding potential exactly. Nuclear effects on the bound-muon $g$ factor are also evaluated. We put forward the measurement of the bound-muon $g$ factor via the continuous Stern-Gerlach effect as an independent means to determine the free muons magnetic moment anomaly and mass. The scheme presented enables to increase the accuracy of the mass by more than an order of magnitude

Muonic hydrogen and the proton radius puzzle

The extremely precise extraction of the proton radius by Pohl et al. from the measured energy difference between the 2P and 2S states of muonic hydrogen disagrees significantly with that extracted from electronic hydrogen or elastic electron-proton scattering. This is the proton radius puzzle. The origins of the puzzle and the reasons for believing it to be very significant are explained. Various possible solutions of the puzzle are identified, and future work needed to resolve the puzzle is discussed.Comment: Minor modifications, some references added, to appear in Annu. Rev. Nucl. Part. Sci. Vol 63 (2013). 60 pages, 5 figures, 1 tabl

Theory of Light Hydrogenlike Atoms

The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion $He^+$, and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium.Comment: 230 pages, 106 figures, 24 tables. Discussion of muonic hydrogen is added, list of references expanded, some minor corrections and amendment

Energy Levels Of Hydrogen-Like Atomsand Fundamental Constants

The present review includes the description of theoretical methods for the investigations of the spectra of hydrogen-like systems. Various versions of the quasipotential approach and the method of the effective Dirac equation are considered. The new methods, which have been developed in the eighties, are described. These are the method for the investigation of the spectra by means of the quasipotential equation with the relativistic reduced mass and the method for a selection of the logarithmic corrections by means of the renormalization group equation. The special attention is given to the construction of a perturbation theory and the selection of graphs, whereof the contributions of different orders of $\alpha$, the fine structure constant, to the energy of the fine and hyperfine splitting in a positronium, a muonium and a hydrogen atom could be calculated. In the second part of this article the comparison of the experimental results and the theoretical results concerning the wide range of topics is produced. They are the fine and hyperfine splitting in the hydrogenic systems, the Lamb shift and the anomalous magnetic moments of an electron and a muon. Also, the problem of the precision determination of a numerical value of the fine structure constant, connected with the above topics, is discussed.Comment: LaTeX file, 68 pp. (figures are available on request

Probing QED Vacuum with Heavy Ions

We recall how nearly half a century ago the proposal was made to explore the structure of the quantum vacuum using slow heavy-ion collisions. Pursuing this topic we review the foundational concept of spontaneous vacuum decay accompanied by observable positron emission in heavy-ion collisions and describe the related theoretical developments in strong fields QED.Comment: 40 pages, Presented by JR at the International Symposium on"New Horizons in Fundamental Physics: From Neutrons Nuclei via Superheavy Elements and Supercritical Fields to Neutron Stars and Cosmic Rays," held to honor Walter Greiner on his 80th birthday at Makutsi Safari Farm, South Africa, November 23-29, 201

Relativistic theory of nuclear structure effects in heavy atomic systems

In this thesis, several aspects of nuclear structure effects and corrections from quantum electrodynamics (QED) in the spectra of hydrogen-like systems are investigated. The first part is concerned with the structure of bound states between a muon and an atomic nucleus, so-called muonic atoms. Here, precise calculations for transition energies and probabilities are presented, using state-of-the-art numerical methods. QED corrections, hyperfine interactions, and the interaction with atomic electrons were evaluated and finite nuclear size effects were incorporated non-perturbatively. Furthermore, new methods for the calculation of higher-order corrections for the hyperfine structure are presented, including a complete calculation of the second-order hyperfine structure and leading-order vacuum polarization corrections for extended electric quadrupole distributions inside the nucleus. In connection with recent x-ray spectroscopic measurements on muonic atoms, the nuclear quadrupole moment of Re-185 and Re-187 is extracted. The second part of this thesis is about the g factor of a bound electron and its dependence on the shape of the nuclear charge distribution. A numerical, non-perturbative approach for the calculation of the corresponding nuclear shape correction is presented and implications for the uncertainties of theoretical predictions are discussed. In particular, the model-uncertainty of the finite-nuclear-size correction to the g factor can be reduced due to the more realistic model of the nuclear charge distribution. Finally, calculations of finite-size and vacuum-polarization corrections to the g factor of a muon bound to a He-4 nucleus significantly contribute to the theoretical prediction on the 10^−9 uncertainty level. As shown in an earlier work, an experimental value of the same accuracy could give access to an improved value of the muon’s mass or magnetic moment anomaly

Dimensional Regularization and Two-loop Vacuum Polarization Operator: Master Integrals, Analytic Results, and Energy Shifts

We Present a Complete Reevaluation of the Irreducible Two-Loop Vacuum-Polarization Correction to the Photon Propagator in Quantum Electrodynamics, i.e. with an Electron-Positron Pair in the Fermion Propagators. the Integration is Carried Out by Reducing the Integrations to a Limited Set of Master Integrals, Which Are Calculated using Integration-By-Parts Identities. Dimensional Regularization is Used in D=4-2ϵ Dimensions, and On-Mass Shell Renormalization is Employed. the One-Loop Effect is Given to Order ϵ, to Be Combined with the 1/ϵ Divergence of the Two-Loop Amplitude. Master Integrals Are Given. Final Evaluations of Two-Loop Energy Shifts for 1S, 2S, and 2P States Are Done Analytically, and Results Are Presented, with an Emphasis on Muonic Hydrogen. for Relativistic Dirac-Coulomb Reference States, Higher-Order Coefficients Are Obtained for the Zα-Expansion. We Compare the Results Obtained to the Existing Literature