Michael I. Eides, Valery A. Shelyuto
Corrections of order $α^3(Zα)^5m$ to the Lamb shift and corrections of order $α^3(Zα)E_F$ to hyperfine splitting generated by the insertions of the three-loop one-particle reducible diagrams with radiative photons in the electron line are calculated. The calculations are performed in the Yennie gauge.
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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 …
We calculate radiative corrections to the Lamb shift of order $α^3(Zα)^5m$ and radiative corrections to hyperfine splitting of order $α^3(Zα)E_F$ generated by the diagrams with insertions of radiative photons and electron polarization loops in the graphs with two external photons. We also obtain the radiative-recoil correction to hyperfine splitting in muonium generated by the diagrams with the $τ$ polarization loop.
Two-loop corrections to Lamb shift and hyperfine splitting in hydrogen via multi-loop methods
本文用 IBP 约化与微分方程等多圈技术重算氢原子中含费米子圈的自能-真空极化混合图，得到 Lamb 位移和超精细分裂相关两圈修正的解析一重积分结果。
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.
The largest contributions to the $n=2$ Lamb-shift, fine structure interval and $2s$ hyperfine structure of muonic hydrogen are calculated by exact numerical evaluations of the Dirac equation, rather than by a perturbation expansion in powers of $1/c$, in the framework of non-relativistic quantum electrodynamics. Previous calculations and the validity of the perturbation expansion for light elements are confirmed. The dependence of the various effects on the nuclear size and model are studied
The 7 standard deviations between the proton rms charge radius from muonic hydrogen and the CODATA-10 value from hydrogen spectroscopy and electron-scattering has caused considerable discussions. Here, we review the theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen combining the published contributions and theoretical approaches. The prediction of these quantities is necessary for the determination of both proton charge and Zemach radii from the two 2S-2P transition frequencies measured in muonic hydrogen.
Probing a Fifth Force in Muonic Atoms through Lamb Shifts and Hyperfine Structure
通过muonic原子的拉姆伯特移和超精细结构研究，探测X17可能存在的第五力，确定muonic氘等为最佳探测目标。
Weak interaction contributions to hyperfine splitting and Lamb shift in light electronic and muonic atoms are calculated. We notice that correction to hyperfine splitting turns into zero for deuterium. Weak correction to the Lamb shift in hydrogen is additionally suppressed in comparison with other cases by a small factor $(1-4\sin^2θ_W)$.
Isotope shifts and hyperfine structure of tungsten were studied in the near UV range. We have used laser induced fluorescence spectroscopy on a pulsed supersonic beam to probe the 5D0 -> 5F1 transition at 384.9 nm, 7S3 -> 7P4 transition at 400.9 nm, and 7S3 -> 7P3 transition at 407.4 nm. Three new magnetic hyperfine constants are reported for 7P3,7P4, and 5F1 states. The isotope shifts of the 384.9 nm transition are presented for the first time, and the isotope shifts of 400.9 nm and 407.4 nm transition are measured with an order of magnitude higher precision compared to the previous measureme…
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 present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncert…
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…
The hyperfine structure (hfs) and the g factor of a bound electron are caused by external magnetic fields. For the hfs, the magnetic field is due to the nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to probe the bound-electron g factor. The self-energy corrections to these effects are more difficult to evaluate than those to the Lamb shift. Here, we describe a numerical approach for both effects in the notoriously problematic regime of hydrogen-like bound systems with low nuclear charge numbers. The calculation is nonperturbative in the binding Coulomb field. Acc…
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…
A Lamb-shift polarimeter, which has been built for a fast determination of the polarization of protons and deuterons of an atomic-beam source and which is frequently used in the ANKE experiment at COSY-Jülich, is shown to be an excellent device for atomic-spectroscopy measurements of metastable hydrogen isotopes. It is demonstrated that magnetic and electric dipole transitions in hydrogen can be measured as a function of the external magnetic field, giving access to the full Breit-Rabi diagram for the $2^2S_{1/2}$ and the $2^2P_{1/2}$ states. This will allow the study of hyperfine structure, $…
We continue the analysis of quantum two-particle bound systems we have started in (Kholmetskii, A.L., Missevitch, O.V. and Yarman, T. Phys. Scr., 82 (2010), 045301), where we re-postulated the Dirac equation for the bound electron in an external EM field based on the requirement of total momentum conservation, when its EM radiation is prohibited. It has been shown that the modified expression for the energy levels of hydrogenic atoms within such a pure bound field theory (PBFT) provides the same gross and fine structure of energy levels like the standard theory. Now we apply the PBFT to the an…
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…
The velocity renormalization group is used to determine ln(alpha) contributions to QED bound state energies. The leading order anomalous dimension for the potential gives the alpha^5 ln(alpha) Bethe logarithm in the Lamb shift. The next-to-leading order anomalous dimension determines the alpha^6 ln(alpha), alpha^7 ln^2(alpha), and alpha^8 ln^3 (alpha) corrections to the energy. These are used to obtain the alpha^8 ln^3(alpha) Lamb shift and alpha^7 ln^2(alpha) hyperfine splitting for Hydrogen, muonium and positronium, as well as the alpha^2 ln(alpha) and alpha^3 ln^2(alpha) corrections to the …
Non-relativisitic second-order corrections to the wave function at origin in muonic and exotic atoms are considered. The corrections are due to the electronic vacuum polarization. Such corrections are of interest due to various effective approaches, which take into account QED and hadronic effects. The wave function at origin plays a key role in the calculation of the pionium lifetime, various finite nuclear size effects and the hyperfine splitting. The results are obtained for the $1s$ and $2s$ states in pionic and muonic hydrogen and deuterium and in pionium, a bound system of $π^+$ and $π^-…
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…
The present knowledge of Lamb shift, fine- and hyperfine structure of the $\mathrm{2S}$ and $\mathrm{2P}$ states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S-2P}$ transition frequencies in muonic deuterium ($μ\mathrm{d}$). A term-by-term comparison of all available sources reveals reliable values and uncertainties of the QED and nuclear structure-dependent contributions to the Lamb shift, which are essential for a determination of the deuteron rms charge radius from $μ\mathrm{d}$. Apparent discrepancies between different sources a…
Laser spectroscopy of the Lamb shift (2S-2P energy difference) in light muonic atoms or ions, in which one negative muon $μ^-$ is bound to a nucleus, has been performed. The measurements yield significantly improved values of the root-mean-square charge radii of the nuclei, owing to the large muon mass, which results in a vastly increased muon wave function overlap with the nucleus. The values of the proton and deuteron radii are 10 and 3 times more accurate than the respective CODATA values, but 7 standard deviations smaller. Data on muonic helium-3 and -4 ions is being analyzed and will give…
Hadronic vacuum polarization in hydrogen-like atoms and ions amid the interplay of recoil and finite-size effects
研究强子真空极化对类氢原子和离子兰姆位移及超精细分裂的贡献，采用色散数据驱动方法，考虑反冲和有限尺寸效应，给出了相关结果，对\(\mu\)H的结果与之前评估有显著偏差。
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