We consider three-loop radiative corrections to the Lamb shift and hyperfine splitting. Corrections of order $α^3(Zα)^5m$ are the largest still unknown contributions to the Lamb shift in hydrogen. We calculated radiative corrections to the Lamb shift and hyperfine splitting generated by the diagrams with insertions of one radiative photon and electron polarization loops in the graphs with two external photons. We also obtained corrections generated by the gauge invariant sets of diagrams with two reducible radiative photon insertions in the electron line and polarization operator insertion in one of the radiative photons, and diagrams with two reducible radiative photon insertions in the electron line and polarization operator insertion in one the external photons. Corrections to the Lamb shift and hyperfine splitting generated by the diagrams with insertions of the three-loop one-particle reducible diagrams with radiative photons in the electron line are calculated in the Yennie gauge.
We evaluate the two-photon exchange corrections to the Lamb shift and hyperfine splitting of S states in electronic hydrogen relying on modern experimental data and present the two-photon exchange on a neutron inside the electronic and muonic atoms. These results are relevant for the precise extraction of the isotope shift as well as in the analysis of the ground state hyperfine splitting in usual and muonic hydrogen.
We consider a set of radiative contributions from one-loop lepton vacuum polarization to the hyperfine splitting of true muonium. Improving previous results, we obtain values for the electron-loop coefficients and extract their leading dependence upon $β=m_μ/m_e$. The coefficients are $C^μ_{20,1{\rm VPCT}}=0.734931603β$, $C^μ_{20,1{\rm VPCA}}=0.551198702β$, and $C^μ_{20,1{\rm VPT}}=0.419149715β$. The mass-independent contribution from three one-loop vacuum polarization is $C_{40,{\rm VPX}}=\frac{1}{127575}\left(-5255-2016π^2+51840ζ(3)\right)$. Contributions from $τ$ up to $\mathcal{O}(m_μα^8)$…
Probing a Fifth Force in Muonic Atoms through Lamb Shifts and Hyperfine Structure
Hebei University（河北大学）；College of Physics Science and Technology, Hebei University（河北大学物理科学与技术学院）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Nanjing University（南京大学）；School of Physics, Nanjing University（南京大学物理学院）；RIKEN Nishina Center, RIKEN（理化学研究所西村中心）；University of Chinese Academy of Sciences（中国科学院大学）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）；Southern Center for Nuclear Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
In this work, we consider the thermal correction to the hyperfine interaction in hydrogen, deuterium, and the $^3$He$^+$ ion. This correction is effectively described by one-loop Feynman graphs in the framework of the quantum electrodynamics theory for bound states at a finite temperature. A simple analysis shows the importance of the obtained results for future prospects for measuring hyperfine splitting. In addition, the application for testing the time variation of fundamental constants is briefly discussed.
Radiative and interelectronic-interaction corrections to the hyperfine splitting in highly charged B-like ions
The ground-state hyperfine splitting values of high-Z boronlike ions are calculated. Calculation of the interelectronic-interaction contribution is based on a combination of the 1/Z perturbation theory and the large-scale configuration-interaction Dirac-Fock-Sturm method. The screened QED corrections are evaluated utilizing an effective screening potential approach. Total hyperfine splitting energies are presented for several B-like ions of particular interest: {}^{45}Sc{}^{16+}, {}^{57}Fe{}^{21+}, {}^{207}Pb{}^{77+}, and {}^{209}Bi{}^{78+}. For lead and bismuth the experimental values of the …
We present a derivation of the last unknown part of the $α^7m$ contribution to the Lamb shift of a two-electron atom, induced by the radiative QED effects beyond the Bethe logarithm. This derivation is performed in the framework of nonrelativistic quantum electrodynamics and is valid for the triplet (spin $S = 1$) atomic states. The obtained formulas are free from any divergences and are suitable for a numerical evaluation. This opens a way for a complete numerical calculation of the $α^7m$ QED effects in helium, which will allow an accurate determination of the nuclear charge radius from meas…
On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $α(Z α)^5$ to the Lamb shift in muonic hydrogen and helium. To construct the interaction potential of particles, which gives the necessary contributions to the energy spectrum, we use the method of projection operators to states with a definite spin. Separate analytic expressions for the contributions of the muon self-energy, the muon vertex operator and the amplitude with spanning photon are obtained. We present also numerical results for these contributions using m…
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasi-degenerate 2P_{1/2} levels which are removed from the 2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift and the hyperfine effects. The van der Waals shift becomes commensurate with the 2S-2P_{3/2} fine-structure splitting only for close approach (R < 100 a_0, where a_0 is the Bohr radius) and one may thus restrict the discussion to the levels with n=2 and J=1/2 to good approximati…
We calculate hard spin-independent three-loop radiative corrections to energy levels in muonium and positronium which are due to radiative insertions in two-photon exchange diagrams. These corrections could be relevant for the new generation of precise $1S-2S$ and $2S-2P$ measurements in muonium and positronium.
Hard spin-independent three-loop radiative contributions to energy levels in positronium generated by the two-photon-exchange diagrams with one-loop radiative insertions in the fermion lines and exchanged photons are calculated. This is a next step in calculations of all corrections of order $mα^7$ inspired by the new generation of precise $1S-2S$ and $2S-2P$ measurements in positronium.
Employing two state-of-the-art methods, multiconfiguration Dirac--Hartree--Fock and second-order many-body perturbation theory, highly accurate calculations are performed for the lowest 272 fine-structure levels arising from the $2s^{2} 2p^{3}$, $2s 2p^{4}$, $2p^{5}$, $2s^{2} 2p^{2} 3l$~($l=s,p,d$), $2s 2p^{3}3l$ ($l=s,p,d$), and $2p^{4} 3l$ ($l=s,p,d$) configurations in nitrogen-like Ge XXVI. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé $g_{J}$-factors, and E1, E2, M1, M2 line strengths, oscillator strengths, and trans…
Energy levels of 30 low-lying states of Lu2+ and allowed electric-dipole matrix elements between these states are evaluated using a relativistic all-order method in which all single, double and partial triple excitations of Dirac-Fock wave functions are included to all orders of perturbation theory. Matrix elements are critically evaluated for their accuracy and recommended values of the matrix elements are given together with uncertainty estimates. Line strengths, transition rates and lifetimes of the metastable 5d(3/2) and 5d(5/2) states are calculated. Recommended values are given for stati…
Comprehensive calculations of energy levels, radiative transition parameters, hyperfine structure constants A$_J$-B$_J$, Landé g$_J$ factors and isotope shifts for Sc XX
Two recent experimental observations at the ATOMKI Institute of the Hungarian Academy of Sciences (regarding the angular emission pattern of electron-positron pairs from nuclear transitions from excited states in 8Be and 4He) indicate the possible existence of a particle of a rest mass energy of roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the process, preceding the emission of the electron-positron pair. Based on the symmetry of the nuclear transitions ($1^+$ to $0^+$ and $0^-$ to $0^+$), the X17 could either be a vector, or a pseudoscalar particle. Here, we calcu…
We have systematically investigated the ground-state hyperfine structure for alkali-metal atoms ^{87}Rb, ^{133}Cs, ^{211}Fr and alkali-metal-like ions ^{135}Ba^+, ^{225}Ra^+, which are of particular interest for parity violation studies. The quantum electrodynamic one-loop radiative corrections have been rigorously evaluated within an extended Furry picture employing core-Hartree and Kohn-Sham atomic potentials. Moreover, the effect of the nuclear magnetization distribution on the hyperfine structure intervals has been studied in detail and its uncertainty has been estimated. Finally, the theo…
We present a detailed study of the Flambaum-Ginges radiative potential method which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms, ions, and molecules over the range 10<=Z<=120, where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s, p, and d waves over the series of alkali atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many…
The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S\rightarrow2P}$ transition frequencies in the muonic helium-3 ion, $\mathrm{μ^3He^+}$. This ion is the bound state of a single negative muon $μ^-$ and a bare helium-3 nucleus (helion), $\mathrm{^3He^{++}}$. A term-by-term comparison of all available sources, including new, updated, and so far unpublished calculations, reveals reliable values and uncertainties of the QED and nuclear structure-d…
An electrodynamical coupled cluster (CC) methodology starting from a covariant formalism and an equal time approximation, and finally based on the Dirac-Fock picture of the electron and positron fields and Coulomb gauge, is given here. The formalism first leads to different physical interactions from the use of an exponential cluster operator for radiative effects. Lamb, Breit and hyperfine interactions are obtained. Next, relativistic many-body effects are determined using the matter cluster in a way familiar from the nonrelativistic CC. This step can be nontrivial. By allowing the matter clu…
In an ensemble of identical atoms, cooperative effects like sub- or superradiance may alter the decay rates and the energy of specific transitions may be shifted from the single-atom value by the so-called collective Lamb shift. While such effects in ensembles of two-level systems are by now well understood, realistic multi-level systems are more difficult to handle. In this work we show that in a system of atoms or nuclei under the action of an external magnetic field, the collective contribution to the level shifts can amount to seizable deviations from the single-atom Zeeman or magnetic hyp…
