Hyperfine Structure Interval Research Articles

High precision in a Fourier-transform spectrum of protactinium: extensive weighted least-squares fits of peak wavenumbers for analysis of fine and hyperfine structure

A Fourier-transform recording of protactinium in the infrared range is reanalysed with high precision in order to determine the hyperfine interaction constants A and B. Starting with a selection of best lines and least-squares fits of hyperfine structure intervals, large systems of linear equations compare experimental hyperfine peak wavenumbers with a theoretical representation. The theoretical representation is based on Ritz’s combination principle and Casimir’s formula according to the existing classification. Weighted least-squares fits allow a discrimination between unperturbed and perturbed data such as blended hyperfine structure components. For the first time, the wavenumbers of the hyperfine components of more than 600 lines are fitted using the characteristics of about 250 levels as parameters. When adding adjustable wavenumber-scale correction parameters, global consistency for the whole IR spectrum is obtained with local limits of about 0.3×10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.3\\,\ imes 10^{-3}$$\\end{document} cm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}. This demonstrates the high precision in both recording and analysis. The values of the fine structure energies are revised. 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Representative examples illustrate extensive results obtained for atomic protactinium. This high precision facilitates further search for new energy levels, and 20 new levels were presented. Foreword The data presented here are the results of a study carried out at the Laboratoire Aimé Cotton (LAC) at Paris-Orsay in the years 2003 and 2004, when I was there for a research stay. At this time, I worked together with Jean-François Wyart and Annie Ginibre on the re-examination of protactinium spectra that have been measured about 30 years earlier and that were available in the form of a printed list of peak wavenumbers and a printed paper chart of the intensity profile. The spectra had already been analysed, but there was still a lot of additional information that could be extracted from the spectra with time and effort. The review of the data, the selection of the data and the step-by-step optimization of the data set took a lot of time. When I returned to Berlin in 2004, we had made good progress, but in principle, it is like a bottomless pit. We continued together to optimize the data and tried to the finishing touches to it. At some point, we decided that we had reached a ‘level of maturity’ where the data could be published. We have discussed a lot about how detailed the text should be. This discussion has dragged on over the years and this project has repeatedly been lost in the stream of other everyday tasks. Every now and then there was a small attempt to return to this topic, but it quickly got lost in the daily hustle and bustle. In 2012, we presented the results at a conference. The death of both of them within two years hit me hard. I very much regret that this work was not published earlier. This special volume was the right motivation for me to finally publish this data. I no longer have access neither to the computer programs used at the time, which ran on large computer systems, nor to the original measurement data. I have not been able to find out what happened to the large quantity of paper (printed list of peak wavenumbers anda printed paper chart of spectra). But I have a bunch of input and output files of the calculations that have become a bit jumbled over the years, which contain a lot of information, as well as our unfinished manuscript. The resulting data contain important information for posterity – particularly since the element is radioactive and the experiments to collect laboratory data are unlikely to be repeated any time soon. I think it is worth publishing these data.Graphic abstractHigh precision FT spectra of Pa: analysis of fine and hyperfine structure

Ab initio calculations of the hyperfine structure of Ra+ and evaluations of the electric quadrupole moment Q of the 209,211,221,223Ra nuclei

The relativistic coupled-cluster method has been employed to calculate the energies, magnetic dipole, electric quadrupole and magnetic octupole hyperfine-structure constants of the low-lying states of Ra+. The validity of our calculations is substantiated by comparing the calculated binding energies and magnetic dipole hyperfine-structure constants with the corresponding available experimental results. The combination of our theoretical results with the available experimental values of the electric quadrupole hyperfine-structure constant, makes it possible to extract the electric quadrupole moments Q of the 209,211,221,223Ra nuclei. Our Q(221Ra) = 1.968(34) and Q(223Ra) = 1.248(22) are consistent with the referenced values 1.978(106) and 1.254(66) from a semi-empirical analysis (1988 Z. Phys. D 11 105), but Q(211Ra) = 0.33(2) is smaller than the referenced value 0.48(4) by about 30%. Furthermore, we also performed a procedure for assessing the contributions of magnetic octupole hyperfine interaction to the hyperfine splitting considering the preliminary value of magnetic octupole moment from the single-particle nuclear structure model. The sensitivity of hyperfine-structure interval measurements in 223Ra+ that can reveal the effect caused by the nuclear octupole moment are found to be on the order of kHz.

New precise spectroscopy of the hyperfine structure in muonium with a high-intensity pulsed muon beam

A hydrogen-like atom consisting of a positive muon and an electron is known as muonium. It is a near-ideal two-body system for a precision test of bound-state theory and fundamental symmetries. The MuSEUM collaboration performed a new precision measurement of the muonium ground-state hyperfine structure at J-PARC using a high-intensity pulsed muon beam and a high-rate capable positron counter. The resonance of hyperfine transition was successfully observed at a near-zero magnetic field, and the muonium hyperfine structure interval of νHFS=4.463302(4)GHz was obtained with a relative precision of 0.9 ppm. The result was consistent with the previous ones obtained at Los Alamos National Laboratory and the current theoretical calculation. We present a demonstration of the microwave spectroscopy of muonium for future experiments to achieve the highest precision.

Theoretical prediction for the muonium hyperfine-structure interval and its accuracy

Because there are new projects on the determination of the hyperfine interval in the ground state of muonium, we revisit different approaches to constructing its theoretical prediction and comparison with experimental data. We discuss a controversy in the accuracy of two recent predictions [Mohr et al., Rev. Mod. Phys. 88, 035009 (2016), and Eides, Phys. Lett. B 795, 113 (2019)] and produce a constraint on possible systematic errors in the determination of the muonium hyperfine-structure interval interval theoretically or experimentally. In particular, a possible additional theoretical term, that may be either a missing ``regular'' theoretical contribution or a contribution due to new physics, is estimated as $\ensuremath{-}0.14(52)\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}$. The constraint is based on all available data through a least-squares-adjustment procedure, including all their correlations. The result is close to the one of Eides [Phys. Lett. B 795, 113 (2019)].

Performance evaluation of a silicon strip detector for positrons/electrons from a pulsed a muon beam

A high-intensity pulsed muon beam is becoming available at the at the Japan Proton Accelerator Research Complex (J-PARC). Many experiments to study fundamental physics using this high-intensity muon beam are proposed. An experiment to measure the muon magnetic moment anomaly (g−2) and the muon electric dipole moment (EDM) is one of these experiments and it requires a tracking detector for positrons from muon decay. Fine segmentation is required in a detector to tolerate the high rate of positrons. The time resolution is required to be much better than the muon anomalous spin precession period while a buffer depth of a front-end electronics needs to be much longer than the accelerated muon lifetime. Requirements of this detector also meet requirements of a measurement of the muonium hyperfine structure interval at the J-PARC and another experiment to measure the proton charge radius at Tohoku University. We have developed a single-sided silicon strip sensor with a 190 μm pitch, a front-end electronics with a sampling rate of 200 MHz and a buffer memory depth of 8192, and a data acquisition system based on DAQ-Middleware for the J-PARC muon g−2/EDM experiment. We have fabricated detector modules consisting of this sensor and the front-end electronics. Performance of fabricated detector modules was evaluated at a laboratory and a beam test using the positron beam at Tohoku University. The detector is confirmed to satisfy all requirements of the experiments except for the time walk, which will be solved by the next version of a front-end electronics.

Hyperfine structure of P states in muonic ions of lithium, beryllium, and boron

We calculate hyperfine structure intervals $\Delta E^{hfs}(2P_{1/2})$ and $\Delta E^{hfs}(2P_{3/2})$ for P-states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method of projection operators on states with definite quantum numbers of total atomic momentum F and total muon momentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders $\alpha^4$, $\alpha^5$ and $\alpha^6$. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data of the CREMA collaboration.

Hyperfine splitting of P-states in light muonic ions

We calculate hyperfine structure intervals for P–states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method ofprojection operators on states with definite quantum numbers of total atomic momentum F and total muonmomentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders α4, α5 and α6. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data.

Ground-state hyperfine splitting for Rb, Cs, Fr, Ba+ , and Ra+

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 theoretical description of the hyperfine structure has been completed with full many-body calculations performed in the all-orders correlation potential method.

Theory of the hyperfine structure of the S states of muonic tritium

The hyperfine structure of the energy spectrum of the S levels of muonic tritium has been calculated using the quasi-potential method in quantum electrodynamics (QED). The α5- and α6-order effects on the polarization of vacuum, the structure and recoil of the nucleus, and relativistic corrections have been taken into account. The obtained numerical values of hyperfine splittings of 239.819 meV (1S state) and 29.965 meV (2S state) can be treated as reliable estimates for comparing with future experimental data of the CREMA collaboration, and hyperfine structure interval Δ12 = 8ΔE hfs (2S)–ΔE hfs (1S) =–0.100 meV can be used for verifying the QED predictions. The resultant precision values of hyperfine splitting are also important for calculating the rates of formation of (μ dt) mesomolecules in muonic catalysis reactions.

New precise measurement of muonium hyperfine structure interval at J-PARC

MuSEUM is an international collaboration aiming at a new precise measurement of the muonium hyperfine structure at J-PARC (Japan Proton Accelerator Research Complex). Utilizing its intense pulsed muon beam, we expect a ten-fold improvement for both measurements at high magnetic field and zero magnetic field. We have developed a sophisticated monitoring system, including a beam profile monitor to measure the 3D distribution of muonium atoms to suppress the systematic uncertainty.

Hyperfine structure ofPstates in muonic deuterium

On the basis of quasipotential approach to the bound state problem in quantum electrodynamics we calculate hyperfine structure intervals Delta E^{hfs}(2P_{1/2}) and Delta E^{hfs}(2P_{3/2}) for P-states in muonic deuterium. The tensor method of projection operators for the calculation of the hyperfine structure of P-states with definite quantum numbers of total atomic momentum F and total muon momentum j in muonic deuterium is formulated. We take into account vacuum polarization, relativistic, quadrupole and structure corrections of orders alpha^4, alpha^5 and alpha^6. The obtained numerical values of hyperfine splittings are useful for the analysis of new experimental data of the CREMA collaboration regarding to muonic deuterium.

Сверхтонкая структура $S$-состояний мюонного дейтерия

В рамках квазипотенциального метода в квантовой электродинамике вычислены поправки порядка $\alpha^5$ и $\alpha^6$ в сверхтонкой структуре $S$-состояний мюонного дейтерия. Учтены релятивистские поправки, эффекты поляризации вакуума в первом, втором и третьем порядках теории возмущений, эффекты структуры и поправки на отдачу. Полученные численные значения сверхтонких расщеплений $\Delta E^{hfs}(1S)=50.2814$ мэВ ($1S$-состояние) и $\Delta E^{hfs}(2S)=6.2804$ meV ($2S$-состояние) можно использовать для сравнения с будущими экспериментальными данными коллаборации CREMA. Интервал сверхтонкой структуры $\Delta_{12}=8\Delta E^{hfs}(2S)- \Delta E^{hfs}(1S)=-0.0379$ meV можно использовать для прецизионной проверки квантовой электродинамики.

Hyperfine structure ofSstates in muonic deuterium

On the basis of quasipotential method in quantum electrodynamics we calculate corrections of order $\alpha^5$ and $\alpha^6$ to hyperfine structure of S-wave energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\Delta E^{hfs}(1S)=50.2814$ meV (1S state) and $\Delta E^{hfs}(2S)=6.2804$ meV (2S state) represent reliable estimate for a comparison with forthcoming experimental data of CREMA collaboration. The hyperfine structure interval $\Delta_{12}=8\Delta E^{hfs}(2S)-\Delta E^{hfs}(1S)=-0.0379$ meV can be used for precision check of quantum electrodynamics predictions for muonic deterium.

Critically Evaluated Energy Levels and Spectral Lines of Singly Ionized Indium (In II).

A comprehensive list of the best measured wavelengths in the In II spectrum has been compiled. Uncertainties of the wavelength measurements have been analyzed, and existing inconsistencies have been resolved. An optimized set of fine-structure energy levels that fits all observed wavelengths has been derived. Uncertainties of the energy level values have been reduced by an order of magnitude. An improved value of the ionization limit of In II has been determined by fitting quantum-defect and polarization formulas for several series of levels. Intensities of lines observed by different authors have been analyzed and converted to a uniform scale. A set of recommended values of radiative transition rates has been critically compiled, and uncertainties of these rates have been estimated. The hyperfine structure interval in the 5s 2S ground state of In III has been determined from the measurements of the 5sng and 5snh series in In II.

Hyperfine structure interval of the2sstate of hydrogenlike atoms and a constraint on a pseudovector boson with mass below 1 keV/c2

A constraint on a spin-dependent interaction, induced by a pseudovector light boson, is presented. The interaction includes a Yukawa-type contribution $\ensuremath{\alpha}{}^{\ensuremath{''}}({\mathbf{s}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{s}}_{2}){e}^{\ensuremath{-}\ensuremath{\lambda}r}/r$ and a contact spin-spin term. To disentangle the long-range and contact terms we utilize experimental data on the $1s$ and $2s$ hyperfine intervals for light two-body atoms and construct a specific difference $8\ifmmode\times\else\texttimes\fi{}{E}_{\mathrm{hfs}}(2s)\ensuremath{-}{E}_{\mathrm{hfs}}(1s)$. That allows one to constrain the spin-dependent coupling constant $\ensuremath{\alpha}{}^{\ensuremath{''}}$ of an electron-nucleus Yukawa-type interaction in hydrogen, deuterium, and the helium-3 ion at the level below a part in ${10}^{16}$. The derived constraint is related to the range of masses below $4 \mathrm{keV}/{c}^{2}$. The combined constraint including the contact terms is also presented.

Hyperfine structure of S- and P-wave states in muonic-helium ion

Corrections of order α 5 and α 6 to the hyperfine structure of S- and P-wave energy levels of the muonic-helium ion are calculated. Electron-vacuum-polarization effects, corrections for the nuclear structure, and recoil effects are taken into account. The numerical values obtained for respective hyperfine splitting, −1334.73 meV (1S), −166.64 meV (2S), −58 712.90 µeV (2P 1/2), and −24 290.69 µeV (2P 3/2), can be viewed as a reliable estimate for a comparison with experimental data, and the hyperfine-structure interval of Δ12 = 8ΔE hfs(2S) − ΔE hfs(1S) = 1.59 meV can be used to test QED predictions.

A critical compilation of experimental data on spectral lines and energy levels of hydrogen, deuterium, and tritium

For more than 50 years, Charlotte Moore’s compilation of atomic energy levels and its subsequent revisions have been the standard source of reference data for the spectra of hydrogen and its isotopes. In those publications, theoretical data based on quantum-electrodynamic calculations have been given. This reflects the fact that the theory of the hydrogen spectrum has been perfected to an extent far exceeding the capabilities of the best measurements. However, rapid advances in the techniques of laser spectroscopy and optical frequency metrology have recently put experiments on a par with theory in terms of precision. This calls for construction of new comprehensive data sets for H, D, and T that summarize the latest experimental work and can be directly compared with the modern theoretical reference data. The present work compiles several tens of recent measurements of the hydrogen, deuterium, and tritium fine and hyperfine structure intervals and presents sets of energy levels and Ritz wavelengths derived from those measurements. Data exist for the fine structure of energy levels of hydrogen and deuterium up to principal quantum number n = 12. For higher lying levels, there are many observed lines with unresolved fine structure. From those observations, level centers (centers of the fine structure) are derived by a least-squares optimization, and Ritz wavelengths of series with upper levels up to n = 40 are obtained. For tritium, the n = 2 and 3 energy level intervals are derived from experimental observations.

Electron Self-Energy in the Presence of a Magnetic Field: Hyperfine Splitting andgFactor

A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known Zalpha-expansion coefficients is determined. For the 3He+ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.

Hyperfine structure of the S levels of the muonic helium ion

Corrections of the α5 and α6 orders to the energy spectrum of the hyperfine splitting of the 1S and 2S levels of the muonic helium ion are calculated with the inclusion of the electron vacuum polarization effects, nuclear-structure corrections, and recoil effects. The values ΔE hfs(1S) = −1334.56 meV and ΔE hfs(2S) = −166.62 meV obtained for hyperfine splitting values can be considered as reliable estimates for comparison with experimental data. The hyperfine structure interval Δ12 = 8ΔE hfs(2S) − ΔE hfs(1S) = 1.64 meV can be used to verify QED predictions.

Hyperfine structure of the metastableP32state of alkaline-earth-metal atoms as an accurate probe of nuclear magnetic octupole moments

Measuring the hyperfine structure (HFS) of long-lived ${^{3}P}_{2}$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in $^{87}\text{S}\text{r}$ needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. The results of similar analyses for $^{9}\text{B}\text{e}$, $^{25}\text{M}\text{g}$, and $^{43}\text{C}\text{a}$ are also reported.