Savely G. Karshenboim
The usefulness of study of hyperfine splitting in the hydrogen atom is limited on a level of 10 ppm by our knowledge of the proton structure. One way to go beyond 10 ppm is to study a specific difference of the hyperfine structure intervals 8 Delta nu_2 - Delta nu_1. Nuclear effects for are not important this difference and it is of use to study higher-order QED corrections.
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An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For helium-like ions, in particular, we propose to measure either the angular distribution or polarization of the $1s2p~^{3}P_{1}, F \rightarrow 1s^{2}~^{1}S_{0}, F_{f}$ emission following the stimulated decay of the initial $1s2s~^{1}S_{0}, F_{i}$ level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depends on the (relative) \textit{splitting} of the partially overlapping hyperfine $1s2p~^{3}P_{1}, F$ resonances an…
On hyperfine structure of the rotationally excited $1 s_μ n\ell_{e}$-states in helium muonic atoms
本文提出新方法推导公式，用于计算三体氦介子原子中转动激发态的超精细结构分裂，填补了该领域空白。
Using a newly developed laser-microwave-laser resonance method, we observed a pair of microwave transitions between hyperfine levels of the $(n,L)=(37,35)$ state of antiprotonic helium. This experiment confirms the quadruplet hyperfine structure due to the interaction of the antiproton orbital angular momentum, the electron spin and the antiproton spin as predicted by Bakalov and Korobov. The measured frequencies of $ν_{\text HF}^+ =12.89596 \pm 0.00034$ GHz and $ν_{\text HF}^- =12.92467 \pm 0.00029$ GHz agree with recent theoretical calculations on a level of $ 6 \times10^{-5}$.
Hyperfine structure splitting for the triplet $2^{3}S(L = 0)-$state in the two-muonic helium ${}^{3}$He $μ_{2}$ atom
本研究高精度计算了双μ子氦原子中三重态 $2^{3}S$ 态的超精细分裂，结果为 $5.1623403103010 \times 10^{7}$ MHz，不确定度仅 $\pm 10$ Hz，源于μ子壳层与核自旋相互作用。
Recent progress in the spectroscopy of antiprotonic helium has allowed for measuring the separation between components of the hyperfine structure (HFS) of the (37,35) metastable states with an accuracy of 300 MHz, equivalent to a relative accuracy of 3x10^{-5}. The analysis of the uncertainties of the available theoretical results on the antiprotonic helium HFS shows that the accuracy of the value of the dipole magnetic moment of the antiproton (currently known to only 0.3 %) may be improved by up to 2 orders of magnitude by measuring the splitting of appropriately selected components of the H…
We report on preliminary results from a systematic study of the hyperfine (HF) structure of antiprotonic helium. This precise measurement which was commenced in 2006, has now been completed. Our initial analysis shows no apparent density or power dependence and therefore the results can be averaged. The statistical error of the observable M1 transitions is a factor of 60 smaller than that of three body quantum electrodynamic (QED) calculations, while their difference has been resolved to a precision comparable to theory (a factor of 10 better than our first measurement). This difference is sen…
We report the first measurements of the inelastic spin exchange collision rate between the Hyperfine (HF) levels of antiprotonic helium. We measure the time dependent evolution of the (37, 35) substates to obtain an inelastic collision rate which qualitatively agrees with recent theoretical calculations. We evaluate these results by using the obtained rate as a parameter in a rigorous simulation which we then compare to to previously measured data. We find that our measurement slightly underestimates the collision rate and therefore conclude that the actual value most probably falls within the…
In this work we describe the latest results for the measurements of the hyperfine structure of antiprotonic helium-3. Two out of four measurable super-super-hyperfine SSHF transition lines of the (n,L)=(36,34) state of antiprotonic helium-3 were observed. The measured frequencies of the individual transitions are 11.12548(08) GHz and 11.15793(13) GHz, with an increased precision of about 43% and 25% respectively compared to our first measurements with antiprotonic helium-3 [S. Friedreich et al., Phys. Lett. B 700 (2011) 1--6]. They are less than 0.5 MHz higher with respect to the most recent t…
The one-loop self-energy correction to the hyperfine structure splitting of the 1s and 2s states of hydrogenlike ions is calculated both for the point and finite nucleus. The results of the calculation are combined with other corrections to find the ground state hyperfine splitting in lithiumlike ^{209}Bi^{80+} and ^{165}Ho^{64+}.
Improved calculation of the hyperfine structure of muonic helium
本文通过二阶微扰理论计算μ子氦超精细结构的新修正，减小了理论值与实验测量的差异。
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.
We have applied an optical method to the measurement of the 2S hyperfine interval in atomic hydrogen. The interval has been measured by means of two-photon spectroscopy of the 1S-2S transition on a hydrogen atomic beam shielded from external magnetic fields. The measured value of the 2S hyperfine interval is equal to 177 556 860(15) Hz and represents the most precise measurement of this interval to date. The theoretical evaluation of the specific combination of 1S and 2S hyperfine intervals D_21 is in moderately good agreement with the value for D_21 deduced from our measurement.
Theoretical investigations of the hyperfine structure of the hydrogen molecular ion (one electron and two protons) are discussed. The nuclear spin-rotation interaction has been found to be of the same sign as in the hydrogen molecule and the hyperfine transition frequencies can be accurately predicted. With measurements of the hyperfine structure of the deuterium molecular ion (or of HD+) it should be possible to obtain a value of the deuteron quadrupole moment that could be compared with the values obtained from the deuterium molecule and from nuclear theory.
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.
The current status of the determination of corrections to the hyperfine splitting of the ground state in hydrogen is considered. Improved calculations are provided taking into account the most recent value for the proton charge radius. Comparing experimental data with predictions for the hyperfine splitting, the Zemach radius of the proton is deduced to be $1.045(16)$ fm. Employing exponential parametrizations for the electromagnetic form factors we determine the magnetic radius of the proton to be $0.778(29)$ fm. Both values are compared with the corresponding ones derived from the data obtai…
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.
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 ground state hyperfine splitting values of high Z hydrogenlike ions are calculated. The relativistic, nuclear and QED corrections are taken into account. The nuclear magnetization distribution correction (the Bohr-Weisskopf effect) is evaluated within the single particle model with the g_{S}-factor chosen to yield the observed nuclear moment. An additional contribution caused by the nuclear spin-orbit interaction is included in the calculation of the Bohr-Weisskopf effect. It is found that the theoretical value of the wavelength of the transition between the hyperfine splitting components …
We consider a simplified model of the optical multi-pass cavity that is being currently developed by the FAMU collaboration for the measurement of the hyperfine splitting in the ground state of muonic hydrogen and of the Zemach radius of the proton. The model is focused on the time distribution of the events of laser-stimulated hyperfine transitions in the muonuc atom and may be helpful in the preliminary design of the FAMU experimental set-up and, more generally, in the optimization of multi-pass optical cavities for experiments with pulsed lasers.
NRQED approach to the fine and hyperfine structure corrections of order m$α$ 6 and m$α$ 6 (m/M)-Application to the hydrogen atom The NRQED approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m$α$ 6 and m$α$ 6 (m/M). Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, and may be used for studying more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used …
The hyperfine structures of the ground states in the ${}^{3}$He$^{2+} μ^{-} e^{-}$ and ${}^{4}$He$^{2+} μ^{-} e^{-}$ helium-muonic atoms are investigated with the use of highly accurate variational wave functions. The differences between corresponding levels of hyperfine structure (i.e. hyperfine splittings) are determined to very high numerical accuracy. In particular, we have found that the hyperfine structure splitting in the ground state of the ${}^{4}$He$^{2+} μ^{-} e^{-}$ atom is $Δν\approx 4464.55454(3)$ $MHz$, while analogous splitting for the ${}^{3}$He$^{2+}μ^{-}e^{-}$ atom is $Δν\ap…
Vacuum Polarization Effects in the Hyperfine Splitting of Hydrogen Like Ions
本文研究了类氢离子超精细结构中由真空极化引起的能级修正，分别计算了轻子型和强子型VP对波函数与磁势的影响，并探讨了不同核模型下结果的不确定性。
An optical measurement of the 2S hyperfine interval in atomic hydrogen using two-photon spectroscopy of the 1S-2S transition gives a value of 177 556 834.3(6.7) Hz. The uncertainty is 2.4 times smaller than achieved by our group in 2003 and more than 4 times smaller than for any independent radio-frequency measurement. The specific combination of the 2S and 1S hyperfine intervals predicted by QED theory $D_{21}=8 f_{\rm HFS}({2S}) - f_{\rm HFS}({1S})=48 953(3)$ Hz is in good agreement with the value of 48 923(54) Hz obtained from this experiment.
Relativistic nuclear recoil effects in hyperfine splitting of hydrogenic systems
本文计算了氢样体系超精细分裂中因有限核质量引起的修正，发现与Bodwin和Yennie的先前结果存在矛盾，并在氢中测量中发现2σ偏差，可能表明质子结构修正存在问题。
The antihydrogen programme of the ASACUSA collaboration at the antiproton decelerator of CERN focuses on Rabi-type measurements of the ground-state hyperfine splitting of antihydrogen for a test of the combined Charge-Parity-Time symmetry. The spectroscopy apparatus consists of a microwave cavity to drive hyperfine transitions and a superconducting sextupole magnet for quantum state analysis via Stern-Gerlach separation. However, the small production rates of antihydrogen forestall comprehensive performance studies on the spectroscopy apparatus. For this purpose a hydrogen source and detector …
The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$. In particular, we have fond that for the $e^{+}[{}^3$He$(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$, 76466.5308 $MHz$ and 5824.4019 $MHz$. In the $e^{+}[{}^4$He$(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.
Improved Measurements of Muonic Helium Ground-State Hyperfine Structure at a Near-Zero Magnetic Field
该研究利用日本强脉冲负μ子束，在近零磁场下首次以CH4为电子供体改进测量μ子氦-4基态超精细结构，获得更精确的Δν值，并检验了同位素效应与CPT不变性。
We revisit the $m α^6 (m/M)$ order corrections to the hyperfine splitting in the H$_2^+$ ion, and find a hitherto unrecognized second-order relativistic contribution associated with the vibrational motion of the nuclei. Inclusion of this correction term produces theoretical predictions which are in excellent agreement with experimental data [K. B. Jefferts, Phys.\ Rev.\ Lett.\ \textbf{23}, 1476 (1969)], thereby concluding a nearly fifty years long theoretical quest to explain the experimental results within their 1-ppm error. The agreement between theory and experiment corroborates the proton …
The purpose of this article is twofold. First, we attempt to give a brief overview of the different application areas of quantum electrodynamics (QED). These include fundamental physics (prediction of atomic energy levels), where the atom may be exposed to additional external fields (hyperfine splitting and g factor). We also mention QED processes in highly intense laser fields, and more applied areas like Casimir and Casimir--Polder interactions. Both the unifying aspects as well as the differences in the the theoretical treatment required by these application areas (such as the treatment of …
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…
This study addresses the effect of the magnetic hyperfine interaction on the relativistic H1s wave functions. These are used to calculate the electric, magnetic, and confinement force densities acting on the 1s electron. The magnetic field couples Dirac equations for different angular momenta. These are solved numerically for the hyperfine singlet and triplet, as well as for a classical magnetic dipole. In the singlet ground state the hyperfine interaction shifts the electron density toward the proton. A similar shift is found for the classical dipole, and an opposite shift for the triplet. Th…
We present tables for the bound-state energies for atomic hydrogen. The tabulated energies include the hyperfine structure, and thus this work extends the work of Rev. Mod. Phys. {\bf 84}, 1527 (2012), which excludes hyperfine structure. The tabulation includes corrections of the hyperfine structure due to the anomalous moment of the electron, due to the finite mass of the proton, and due to off-diagonal matrix elements of the hyperfine Hamiltonian. These corrections are treated incorrectly in most other works. Simple formulas valid for all quantum numbers are presented for the hyperfine corre…
Precision measurements of muonium and muonic helium hyperfine structure at J-PARC
MuSEUM 合作组在 J-PARC 利用脉冲 μ 子束精密测量 μ 子素与 μ 氦基态 HFS，以检验 QED、确定 μ 子参数并提升测量精度。
We report the initial results from a systematic study of the hyperfine (HF) structure of antiprotonic helium (n,l) = (37,~35) carried out at the Antiproton Decelerator (AD) at CERN. We performed a laser-microwave-laser resonance spectroscopy using a continuous wave (cw) pulse-amplified laser system and microwave cavity to measure the HF transition frequencies. Improvements in the spectral linewidth and stability of our laser system have increased the precision of these measurements by a factor of five and reduced the line width by a factor of three compared to our previous results. A compariso…
We study the proton-hydrogen collision in the energy range from 0 to 5 K where the hyperfine structure of the hydrogen atom is important. The proper multichannel treatment of the hyperfine structure is found to be crucial at cold temperatures compared to the elastic approximation used for higher temperatures. Both elastic and hyperfine-changing inelastic processes are investigated using the newly developed multichannel quantum-defect theory (MQDT) as well as the traditional coupled-channel numerical method. Cross section results from the two methods coincide well throughout the energy range. T…
We find a new correction to the hydrogen atom ground state hyperfine energy levels splitting in magnetic field. It can be interpreted as magnetic focusing of the wave function at the origin. The effect might be within the reach of experiment.
The ASACUSA collaboration is developing a polarized beam of antihydrogen atoms to precisely determine the ground-state hyperfine structure for studies of CPT and Lorentz invariance. Using a beam of ordinary hydrogen, measurements of both the $σ$ and $π$-transition have been performed, investigating orientation-dependent SME coefficients. Furthermore a first hyperfine experiment with a beam of deuterium is being prepared.
We consider the most accurate tests of bound state QED theory of the hyperfine splitting in two-body atoms related to the HFS interval of the 1s state in muonium and positronium and the 2s state in hydrogen, deuterium and the helium-3 ion. We summarize their QED theory and pay special attention to involved effects of strong interactions and to recent optical measurements of the 2s HFS interval in hydrogen and deuterium. We present results for specific ratios of the 1s-2s frequencies in hydrogen and deuterium which happen to be among the most accurately measured and calculated quantities.
Direct muon transfer in low-energy collisions of the muonic hydrogen H$_μ$ and helium (He$^{++}$) is considered in a three-body quantum-mechanical framework of coordinate-space integro-differential Faddeev-Hahn-type equations within two- and six-state close coupling approximations. The final-state Coulomb interaction is treated without any approximation employing appropriate Coulomb waves in the final state. The present results agree reasonably well with previous semiclassical calculations.
Antihydrogen, the lightest atom consisting purely of antimatter, is an ideal laboratory to study the CPT symmetry by comparison to hydrogen. With respect to absolute precision, transitions within the ground-state hyperfine structure (GS-HFS) are most appealing by virtue of their small energy separation. ASACUSA proposed employing a beam of cold antihydrogen atoms in a Rabi-type experiment to determine the GS-HFS in a field-free region. Here we present a measurement of the zero-field hydrogen GS-HFS using the spectroscopy apparatus of ASACUSA's antihydrogen experiment. The measured value of $ν_…
The fully relativistic theory of the Zeeman splitting of the $1s$ hyperfine structure levels in hydrogenlike ions is considered for the magnetic field magnitude in the range from 1 to 10 T. The second-order corrections to the Breit -- Rabi formula are calculated and discussed. The results can be used for a precise determination of nuclear magnetic moments from $g$ factor experiments.
The (3p - 1s) X-ray transition to the muonic hydrogen ground state was measured with a high resolution crystal spectrometer. A Doppler effect broadening of the X-ray line was established which could be attributed to different Coulomb de-excitation steps preceding the measured transition. The assumption of a statistical population of the hyperfine levels of the muonic hydrogen ground state was directly confirmed by the experiment and measured values for the hyperfine splitting can be reported. The results allow a decisive test of advanced cascade model calculations and establish a method to ext…
The prospects of tests of CPT symmetry using precision spectroscopy of antihydrogen are discussed with special emphasis on the ground-state hyperfine structure, a measurement of which is the aim of the ASACUSA collaboration at the AD/ELENA facility of CERN. Ongoing parallel experiments using hyperfine spectroscopy of hydrogen and deuterium aiming at studying Lorentz invariance by determining coefficients of the Standard Model Extension framework are described.
The contribution from the axial-vector meson exchange to the potential of the muon-proton interaction in muonic hydrogen induced by anomalous axial-vector meson coupling to two photon state is calculated. It is shown that such contribution to the hyperfine splitting in muonic hydrogen is large and important for a comparison with precise experimental data. In the light of our result, the proton radius "puzzle" is discussed.
We develop an approach to describing coherent Compton scattering of photons in the keV energy range from hydrogen and helium atoms based on a relativistic version of the AA-approximation within the standard perturbative S-matrix formalism. The resulting formulas for the cross section take into account the effects of the electron boundness and correctly reproduce the behavior of the cross section at large photon energies, where it goes to Thomson formula, which coincides with the Klein-Nishina-Tamm formula for the cross section in the non-relativistic limit.
The ASACUSA collaboration at the Antiproton Decelerator of CERN aims at a precise measurement of the antihydrogen ground-state hyperfine structure as a test of the fundamental CPT symmetry. A beam of antihydrogen atoms is formed in a CUSP trap, undergoes Rabi-type spectroscopy and is detected downstream in a dedicated antihydrogen detector. In parallel measurements using a polarized hydrogen beam are being performed to commission the spectroscopy apparatus and to perform measurements of parameters of the Standard Model Extension (SME). The current status of antihydrogen spectroscopy is reviewe…
This paper describes measurements of the hyperfine structure of two antiprotonic atoms that are planned at the Antiproton Decelerator (AD) at CERN. The first part deals with antiprotonic helium, a three-body system of alpha-particle, antiproton and electron that was previously studied at LEAR. A measurement will test existing three-body calculations and may - through comparison with these theories - determine the magnetic moment of the antiproton more precisely than currently available, thus providing a test of CPT invariance. The second system, antihydrogen, consisting of an antiproton and a …
We study the ionization process involving antiproton and hydrogen in the energy range between 0.1 keV to 500 keV, using single center close coupling approximation. We construct the scattering wave function using B-spline bases. The results obtained for ionization of atomic hydrogen are compared with other existing theoretical calculations as well as with the available experimental data. The present results are found to be encouraging. We also employed this method to study the ionization of ionized helium in the energy range between 1 and 500 keV. On comparision, the present results are found t…
We present the leading-order prediction of baryon chiral perturbation theory for the proton polarizability contribution to the 2S hyperfine splitting in muonic hydrogen, and compare with the results of dispersive calculations.
We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and pola…
By solving the two-body Schordinger equation in a very high precise nonperturbative numerical (NPnum) way, we reexamine the contributions of fine, hyperfine structure splittings of muonic hydrogen based on the Breit potential. The comparison of our results with those by the first order perturbative theory ($^{1st}$PT) in the literature shows, when the structure of proton is considered, the differences between the results by the $^{1st}$PT and NPnum methods are small for the fine and hyperfine splitting of $2P$ state, while are about $-0.009$ meV and $0.08$ meV for the $F=1$ and total hyperfine…
Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems
提出一种在$Z\,α$上精确的QED方法推导类氢系统核反冲修正，并完成超精细分裂$O(m/M)$纯反冲项的示例推导与$(Z\,α)^5$结果验证。
We show that the non-spherical charge distribution of the proton manifests itself in hydrogen hyperfine splitting as an increase (in absolute value) of the proton Zemach radius and polarization contributions.
State-dependent quantum electrodynamic corrections are evaluated for the hyperfine splitting of nS states for arbitrary principal quantum number n. The calculations comprise both the self-energy and the vacuum-polarization correction of order alpha(Z alpha)^2 E_F and the recoil correction of order (Z alpha)^2 (m/M) E_F. Higher-order corrections are summarized and partly reevaluated as well. Accurate predictions for hydrogen hyperfine splitting intervals of nS states with n=2,...,8 are presented. The results obtained are important due to steady progress in hydrogen spectroscopy for transitions …
The linear polarization of the characteristic photon emission from few-electron ions is studied for its sensitivity with regard to the nuclear spin and magnetic moment of the ions. Special attention is paid, in particular, to the K$α_1$ ($1s 2p_{3/2} ^{1,3}P_{1,2} \to 1s^2 ^1S_0$) decay of selected helium-like ions following the radiative electron capture into initially hydrogen-like species. Based on the density matrix theory, a unified description is developed that includes both, the many-electron and hyperfine interactions as well as the multipole-mixing effects arising from the expansion o…
Relativistic corrections to the hyperfine splitting are calculated for the triplet $2^3S_1$ state of the helium isotope He$^3$. High precision variational wave functions are employed, where the electron-electron correlations are well accounted for. Due to the unknown nuclear structure a comparison with the experimental result is performed via He$^{3+}$ hyperfine splitting. Surprisingly, the second order contribution due to Fermi interaction, in spite of the additional small factor $m/M$, is very significant.
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…
Laser Excitation of Muonic 1S Hydrogen Hyperfine Transition: Effects of Multi-pass Cell Interference
本文研究了多程细胞中干涉效应对μ子氢超精细跃迁概率的影响，提出模型评估最大干涉效应并证明在实验条件下可忽略。
We present a high-precision calculation of the recoil--finite-size correction to the hyperfine splitting (HFS) in muonic and electronic hydrogen based on nucleon electromagnetic form factors obtained from dispersion theory. This will help guide the upcoming searches of the HFS transition in muonic hydrogen, and will allow a precise determination of the polarizability and Zemach radius contributions when this transition is found.
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