In order to explain discrepancies between theoretical predictions and experimental data for the helium fine structure, we check and recalculate all theoretical contributions up to orders mα^7 and m^2/Mα^6. The previous result for the mα^7 correction is improved by a much more accurate calculation of relativistic corrections to the Bethe logarithm. The theoretical values of the 2^3P_0-2^3P_1 and 2^3P_1-2^3P_2 fine structure intervals in helium are, correspondingly, ν_{01} = 29616946.2(1.6) kHz and ν_{12} = 2291177.3(1.6) kHz, with the uncertanties being due to higher-order effects. For the small interval ν_{12}, the theoretical value agrees with the experimental data, whereas for the large interval ν_{01}, a discrepancy of about 3 standard deviations is present.
Calculational results are presented for the fine-structure splitting of the 2^3P state of helium and helium-like ions with the nuclear charge Z up to 10. Theoretical predictions are in agreement with the latest experimental results for the helium fine-structure intervals as well as with the most of the experimental data available for light helium-like ions. Comparing the theoretical value of the 2^3P_0-2^3P_1 interval in helium with the experimental result [T. Zelevinsky et al. Phys. Rev. Lett. 95, 203001 (2005)], we determine the value of the fine-structure constant αwith an accuracy of 31 pa…
We report a calculation of the fine structure splitting in light helium-like atoms, which accounts for all quantum electrodynamical effects up to order α^5 Ry. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.
Improved theoretical predictions for the fine-structure splitting of $2^3P_J$ levels in helium are obtained by the calculation of contributions of order $α^5 Ry$. New results for transition frequencies, $ν_{01} = 29 616 943.01(17)$ kHz and $ν_{12} = 2 291 161.13(30)$ kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.
For decades, improved theory and experiment of the $n=2$ $^3$P fine structure of helium have allowed for increasingly-precise tests of quantum electrodynamics, determinations of the fine-structure constant $α$, and limitations on possible beyond-the-Standard-Model physics. Here we use the new frequency-offset separated-oscillatory-fields (FOSOF) technique to measure the $2^3$P$_2\!\!\to\!2^3$P$_1$ interval. Our result of $2\,291\,176\,590(25)$~Hz represents a major step forward in precision for helium fine-structure measurements.
This paper has been temporarily withdrawn by the authors. In the process of 4He 2P fine structure measurement in a vapor cell, highly nonlinear dependences of 2S_1 - 2P_J intervals on helium density are observed and attributed to light pressure. If total angular momentum of the excited state is not greater than that of the ground state, there are large polarization dependences and variations of shifts with helium pressure that exhibit apparent singularities. A pressure-variable cell may be a better system for control of this effect than an atomic beam. A method of avoiding the shifts for the f…
Spectroscopic measurements of the helium atom are performed to high precision using an atomic beam apparatus and electro-optic laser techniques. These measurements, in addition to serving as a test of helium theory, also provide a new determination of the fine structure constant α. An apparatus was designed and built to overcome limitations encountered in a previous experiment. Not only did this allow an improved level of precision but also enabled new consistency checks, including an extremely useful measurement in 3He. I discuss the details of the experimental setup along with the major chan…
We present recent progress in the calculation of the helium fine-structure splitting of the 2^3P_J states, based on the quantum electrodynamic theory. Apart from the complete evaluation of mα^7 and m^2/Mα^6 corrections, we have performed extensive tests by comparison with all experimental results for light helium-like ions and with the known large nuclear charge asymptotics of individual corrections. Our theoretical predictions are still limited by the unknown mα^8 term, which is conservatively estimated to be 1.7 kHz. However, comparison with the latest experimental result for the 2^3P_0 - 2^…
There is presently disagreement between theory and experiment as well as between different theoretical calculations concerning the fine-structure splitting of the lowest P state of the neutral helium atom. We believe that we have found a minor error in the formulas used by Drake et al. (Can. J. Phys. 80, 1195 (2002)) in their calculations, and we may have an explanation how the error has occurred. To what extent this might resolve (part of) the discrepancy is not known at present.
Agreement between theoretical calculations of atomic structure and spectroscopic measurements is used to constrain possible contribution of exotic spin-dependent interactions between electrons to the energy differences between states in helium-4. In particular, constraints on dipole-dipole interactions associated with the exchange of pseudoscalar bosons (such as axions or axion-like particles, ALPs) with masses $10^{-2}~{\rm eV} \lesssim m \lesssim 10^{4}~{\rm eV}$ are improved by a factor of $\sim 100$. The first atomic-scale constraints on several exotic velocity-dependent dipole-dipole inte…
In this paper the new type of thermal corrections for the helium and helium-like atomic systems are introduced. These are thermal one-photon exchange between the bound electrons and nucleus as well as between the bound electrons induced by the blackbody radiation (BBR). All the derivations are given within the rigorous QED theory. It is shown that these thermal corrections are the same order in powers of $α$ (fine structure constant) as the well-known BBR-induced Stark shift but the different behaviour in temperature. The numerical results presented in this paper make possible to expect their …
In the present paper, we study nonresonant corrections for experimental measurements of the transition frequencies in the helium atom. Having attracted more attention, such effects can make a significant contribution to experiments based on one- and two-photon atomic spectroscopy. The quantum interference effects in the measurements of $2^3S_1-n^3D_1$ ($ n=3,\,4,\,5 $) transition frequencies based on Doppler-free two-photon spectroscopy, are considered as a possible source of current discrepancy between the experimental and theoretical data. We demonstrate that line profile asymmetry caused by…
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine-structure constant $α$. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, $r_1$, $r_2$ and $r = |\vec{r}_1-\vec{r}_2|$. The choice of the exponential basis functions of the form $\exp(-αr_1 -βr_2 -γr)$ allows us to construct an accurate and c…
Collinear Laser Spectroscopy of the $1s2s\,^3\!S_1\rightarrow 1s2p\,^3\!P_{0,2}$ Transitions in Helium-like $^{11}$B$^{3+}$
Institut für Kernphysik, Universität Münster（明斯特大学核物理研究所）；Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）；Helmholtz Research Academy Hesse for FAIR, GSI Helmholtzzentrum für Schwerionenforschung GmbH（黑森州FAIR亥姆霍兹研究院，GSI重离子研究中心有限公司）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Argonne National Laboratory（阿贡国家实验室）
We critically examine the current status of theoretical calculations of the energies, the fine structure, and the isotope shift of the lowest-lying states of helium, searching for unresolved discrepancies with experiments. Calculations are performed within the quantum electrodynamics expansion in powers of the fine structure constant $α$ and the electron-to-nucleus mass ratio $m/M$. For energies, theoretical results are complete through orders $α^6m$ and $α^6m^2/M$, with the resulting accuracy ranging from $0.5$ to $2$~MHz for the $n=2$ states. The fine-structure splitting of the $2^3P$ state …
Precise numerical calculation of radiofrequency intervals between hyperfine sublevels of the $(37,35)$ state of the antiprotonic helium-4 atom is presented. Theoretical consideration includes the QED corrections of order $mα^6$ to the electron spin-orbit interaction. The effective Hamiltonian is derived using the formalism of the nonrelativistic quantum electrodynamics (NRQED).
The recoil, vacuum polarization and electron vertex corrections of first and second orders in the fine structure constant $α$ and the ratio of electron to muon and electron to α-particle masses are calculated in the hyperfine splitting of the $1s^{(e)}_{1/2}2s^{(μ)}_{1/2}$ state of muonic helium atom (μe ^4_2He) on the basis of a perturbation theory. We obtain total result for the muonically excited state hyperfine splitting $Δν^{hfs}=4295.66$ MHz which improves previous calculations due to the account of new corrections and more accurate treatment of the electron vertex contribution.
Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order $α^7m$, where $α$ is the fine-structure constant and $m$ is the electron mass. We make an important step towards the complete calculation of these effects by deriving the most challenging part, which is induced by the virtual photon exchange between all three helium particles, the two electrons, and the nucleus. The complete calculation of the $α^7m$ effect including the radiative corrections will allow comparing of the nuclear charge radii determined from the electronic and …
Corrections to energy levels in light muonic atoms are investigated in order $α^2(Zα)^4m$. We pay attention to corrections which are specific for muonic atoms and include the electron vacuum polarization loop. In particular, we calculate relativistic and relativistic-recoil two-loop electron vacuum polarization contributions. The results are obtained for the levels with $n=1,2$ and in particular for the Lamb shift ($2p_{1/2}-2s_{1/2}$) and fine-structure intervals ($2p_{3/2}-2p_{1/2}$) in muonic hydrogen, deuterium, and muonic helium ions.
We provide an up to date summary of the theory contributions to the 2S-2P Lamb shift and the fine structure of the 2P state in the muonic helium ion $(\mathrm{μ^4He})^+$. This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerland. Individual theory contributions needed for a charge radius extraction are compared and compiled into a consistent summary. The influence of the alpha particle charge distribution on the elastic two-photon exchange is studied to take into account pos…
Splitting Isotope Shift in the $1s2p\,^3\!P_{0,1,2}$ Fine-Structure Triplet in $^{12,13,14}$C$^{4+}$: Experiment and Theory
Institut für Kernphysik, Technische Universität Darmstadt（达姆施塔特工业大学核物理研究所）；Helmholtz Research Academy Hesse for FAIR, GSI Helmholtzzentrum für Schwerionenforschung（黑森FAIR亥姆霍兹研究院，GSI重离子研究中心）；Department of Physics, University of Windsor（温莎大学物理系）；Physics Division, Argonne National Laboratory（阿贡国家实验室物理部）
The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Zalpha)^4 mu^3/m_N^2 is evaluated for muonic hydrogen and deuterium, and muonic helium ions (mu is the reduced mass and m_N is the nuclear mass). Relativistic corrections to vacuum polarization of order alpha (Zalpha)^4 mu are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to vacuum polarization of order alpha (Zα)^5 ln^2(Zalpha) mu^2/m_…
The $1\mathrm{s}n\mathrm{p}\,^3\mathrm{P}_J$ fine structure of high Rydberg states in helium has been measured by microwave spectroscopy of single-photon transitions from $1\mathrm{s}n\mathrm{s}\,^3\mathrm{S}_1$ levels in pulsed supersonic beams. For states with principal quantum numbers in the range from $n=34$ to 36, the $J = 0 \rightarrow 2$ and $J = 1 \rightarrow 2$ fine structure intervals were both observed. For values of $n$ between 45 and 51 only the larger $J = 0 \rightarrow 2$ interval was resolved. The experimental results are in good agreement with theoretical predictions. Detailed…
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 recent 15 parts-per-million (ppm) experiment on muonic hydrogen found a major discrepancy with QED and independent nuclear size determinations. Here we find a significant discrepancy in a different type of exotic atom, a medium-Z nucleus with two electrons. Investigation of the data collected is able to discriminate between available QED formulations and reveals a pattern of discrepancy of almost 6 standard errors of experimental results from the most recent theoretical predictions with a functional dependence proportional to Z^n where n=4. In both the muonic and highly charged systems, the …
The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.
On the basis of the perturbation theory in the fine structure constant $α$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(μ e \ ^3_2He)$. We obtain total result for the ground state hyperfine splitting $Δν^{hfs}=4166.471$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections of orders $α^5$ and $α^6$. The remaining difference between our theoretical result and experi…
