Recently the first laser spectroscopy measurement of the radioactive RaF molecule has been reported by Ruiz \textit{et al.} [Nature \textbf{581}, 396 (2020)]. This and similar molecules are considered to search for the New Physics effects. The radium nucleus is of interest as it is octupole-deformed and has close levels of opposite parity. The preparation of such experiments can be simplified if there are reliable theoretical predictions. It is shown that the accurate prediction of the hyperfine structure of the RaF molecule requires to take into account the finite magnetization distribution inside the radium nucleus. For atoms, this effect is known as the Bohr-Weisskopf (BW) effect. Its magnitude depends on the model of the nuclear magnetization distribution which is usually not well known. We show that it is possible to express the nuclear magnetization distribution contribution to the hyperfine structure constant in terms of one magnetization distribution dependent parameter: BW matrix element for $1s$-state of the corresponding hydrogen-like ion. This parameter can be extracted from the accurate experimental and theoretical electronic structure data for an ion, atom, or molecule without the explicit treatment of any nuclear magnetization distribution model. This approach can be applied to predict the hyperfine structure of atoms and \textit{molecules} and allows one to separate the nuclear and electronic correlation problems. It is employed to calculate the finite nuclear magnetization distribution contribution to the hyperfine structure of the $^{225}$Ra$^+$ cation and $^{225}$RaF molecule. For the ground state of the $^{225}$RaF molecule, this contribution achieves 4\%.
Relativistic ab initio calculations have been performed to assess the suitability of RaF for experimental search of P- and T,P-violating interactions. The parameters of P- and T,P-odd terms of the spin-rotational Hamiltonian have been calculated for the ${^2}Σ$ electronic ground state of RaF molecule. They include the parameter $W_a$, which is critical in experimental search for nuclear anapole moment and the parameters $W_d$ and $W_{\rm SP}$ required to obtain restrictions on the electric dipole moment of the electron and T,P-odd scalar-pseudoscalar interactions, respectively. The parameter $…
We investigate the influence of the spatial extent of the proton magnetization and charge densities on the 2S hyperfine splitting in muonic hydrogen. The use of a non-perturbative relativistic Dirac approach leads to corrections of 15% to values obtained from the perturbative treatment encapsulated by the Zemach radius, which surpass the next-leading order contribution in the perturbation series by an order of magnitude.
The hyperfine splitting in hydrogenlike $^{209}$Bi, $^{203}$Tl, and $^{205}$Tl is calculated with the nuclear magnetization determined from experimental data on the hyperfine splitting in the corresponding muonic atoms. The single-particle and configuration-mixing nuclear models are considered. The QED corrections are taken into account for both electronic and muonic atoms. The obtained results are compared with other calculations and with experiment.
Three models of the nuclear magnetization distribution are applied to predict the hyperfine structure of the hydrogenlike heavy ions and neutral thallium atoms: the uniformly magnetized ball model and single-particle models for the valence nucleon with the uniform distribution and the distribution determined by the Woods-Saxon potential. Results for the hydrogenlike ions are in excellent agreement with previous studies. The application of the Woods-Saxon model is now extended to the neutral systems with the explicit treatment of the electron correlation effects within the relativistic coupled …
We report on our calculations of differential hyperfine anomalies in the nuclear single-particle model for a number of atoms and ions of interest for studies of fundamental symmetries violations. Comparison with available experimental data allows one to discriminate between different nuclear magnetization models, and this data supports the use of the nuclear single-particle model over the commonly-used uniform ball model. Accurate modelling of the nuclear magnetization distribution is important for testing atomic theory through hyperfine comparisons. The magnetization distribution must be adeq…
Nuclear moments, charge radii, and magnetization distribution parameters of Ag isotopes from laser spectroscopy and \textit{ab initio} electronic-structure calculations
Petersburg Nuclear Physics Institute named by B.P. Konstantinov of National Research Centre “Kurchatov Institute”（以B.P.康斯坦丁诺夫命名的国家研究中心“库尔恰托夫研究所”圣彼得堡核物理研究所）；Saint Petersburg State University（圣彼得堡国立大学）；KU Leuven, Instituut voor Kern- en Stralingsfysica（荷语鲁汶大学核与辐射物理研究所）；Centre for Cold Matter, Imperial College London（伦敦帝国理工学院冷物质中心）；State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）
Calculations of the magnetic hyperfine structure rely on the input of nuclear properties -- nuclear magnetic moments and nuclear magnetization distributions -- as well as quantum electrodynamic (QED) radiative corrections for high-accuracy evaluation in heavy atoms. The uncertainties associated with assumed values of these properties limit the accuracy of hyperfine calculations. For example, for the heavy alkali-metal atoms Cs and Fr, these uncertainties may amount collectively to almost 1\% or 2\%, respectively. In this paper we propose a method for removing the dependence of hyperfine struct…
Determination of nuclear moments for many nuclei relies on the computation of hyperfine constants, with theoretical uncertainties directly affecting the resulting uncertainties of the nuclear moments. In this work we improve the precision of such method by including for the first time an iterative solution of equations for the core triple cluster amplitudes into the relativistic coupled-cluster method, with large-scale complete basis sets. We carried out calculations of the energies and magnetic dipole and electric quadrupole hyperfine structure constants for the low-lying states of 229Th^(3+)…
A large-scale configuration-interaction (CI) calculation is reported for the hyperfine splitting of the 2^2S and 3^2S states of ^7Li and ^9Be^+. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with a separate treatment of the QED, nuclear-size, nuclear-magnetization distribution, and recoil corrections. The nonrelativistic limit of the CI results is in excellent agreement with variational calculations. The theoretical values obtained for the hyperfine splitting are complete to the relative order of α^2 and improve upon results of previous studies.
In the unconventional f-electron-associated charge order phase of filled skutterudite PrRu4P12, the low-temperature behaviors of the triplet crystalline-electric-field ground state of Pr ions have been studied by specific heat and magnetization measurements using high quality single crystals. Specific heat shows an anomalous Schottky-type peak structure at 0.30 K in zero field in spite of the absence of any symmetry breaking. Magnetization curve at 0.06 K shows a remarkable rounding below 1 T. It has been revealed that these anomalies provide compelling evidence for the formation of a lattice …
A large-scale relativistic configuration-interaction (CI) calculation is performed for the magnetic-dipole and the electric-quadrupole hyperfine structure splitting in ^{7,6}Li and ^9Be^+. Numerical results for the 2^2S, 3^2S, 2^2P_{1/2}, and 2^2P_{3/2} states are reported. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with separate treatments of the QED, nuclear-magnetization distribution, recoil, and negative-continuum effects.
The hyperfine splitting of the ground and low-energy $3/2^+(7.8 \pm 0.5$ eV) levels in the $^{229}$Th nucleus in muonic atom ($μ^-_{1S_{1/2}}{}^{229}$Th$)^*$ has been calculated considering the distribution of the nuclear magnetization in the framework of collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. It is shown that (a) the hyperfine splitting of the $3/2^+$ isomeric state is anomalously weak, and the reduction of hyperfine structure in comparison with the model of a point nuclear magnetic dipole is close to 100\%, (b) partial inversion of lev…
We report a fourfold improvement in the determination of nuclear magnetic moments for neutron-deficient isotopes of francium-207--213, reducing the uncertainties from 2% for most isotopes to 0.5%. These are found by comparing our high-precision calculations of hyperfine structure constants for the ground states with experimental values. In particular, we show the importance of a careful modeling of the Bohr-Weisskopf effect, which arises due to the finite nuclear magnetization distribution. This effect is particularly large in Fr and until now has not been modeled with sufficiently high accura…
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 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…
The hyperfine splitting of the ground state of selected B-like ions within the range of nuclear charge numbers $Z=49-83$ is investigated in detail. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in $1/Z$. The screened QED corrections are evaluated to all orders in $αZ$ by using an effective potential. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model.
The hyperfine splitting of the ground state of H-, Li-, and B-like ions is investigated in details within the range of nuclear numbers Z = 7-28. The rigorous QED approach together with the large-scale configuration-interaction Dirac-Fock-Sturm method are employed for the evaluation of the interelectronic-interaction contributions of first and higher orders in 1/Z. The screened QED corrections are evaluated to all orders in (αZ) utilizing an effective potential approach. The influence of nuclear magnetization distribution is taken into account within the single-particle nuclear model. The speci…
We have measured the hyperfine splitting of the $7P_{1/2}$ state at the 100 ppm level in Fr isotopes ($^{206g,206m, 207, 209, 213, 221}$Fr) near the closed neutron shell ($N$ = 126 in $^{213}$Fr). The measurements in five isotopes and a nuclear isomeric state of francium, combined with previous determinations of the $7S_{1/2}$ splittings, reveal the spatial distribution of the nuclear magnetization, i.e. the Bohr-Weisskopf effect. We compare our results with a simple shell model consisting of unpaired single valence nucleons orbiting a spherical nucleus, and find good agreement over a range of…
For twenty years research into the anomalies in the HF spectra was going in a wrong direction by fighting the related Bohr-Weisskopf effect. As a way out, the model-independent way is proposed of estimating the nuclear radii from the hyper-fine splitting. The way is based on analogy of HFS to internal conversion coefficients, and the Bohr-Weisskopf effect - to the anomalies in the internal conversion coefficients. This makes transparent It is shown that the parameters which can be extracted from the data are the even nuclear moments of the magnetization distribution. The radii $R_2$ and (for t…
We measure nuclear and electron spin-polarized H and D densities of at least 10$^{19}\, cm^{-3}$ with $\sim$10 ns lifetimes, from the photodissociation of HBr and DI with circularly-polarized UV light pulses. This density is $\sim$6 orders of magnitude higher than that produced by conventional continuous-production methods, and, surprisingly, at least 100 times higher than expected densities for this photodissociation method. We observe the hyperfine quantum beating of the H and D magnetization with a pick-up coil, i.e., the respective 0.7 and 3 ns periodic transfer of polarization from the el…
We investigate the $2\,^3\!S_1$--$2\,^3\!P_J$ ($J = 0, 1, 2$) transitions in $\rm^6Li^+$ using the optical Ramsey technique and achieve the most precise values of the hyperfine splittings of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states, with smallest uncertainty of about 10~kHz. The present results reduce the uncertainties of previous experiments by a factor of 5 for the $2\,^3\!S_1$ state and a factor of 50 for the $2\,^3\!P_J$ states, and are in better agreement with theoretical values. Combining our measured hyperfine intervals of the $2\,^3\!S_1$ state with the latest quantum electrodynamic (Q…
We report the relativistic coupled cluster study of the hyperfine structure and effect of the nuclear magnetization distribution (Bohr-Weisskopf effect) in the $6P_{1/2}$, $6P_{3/2}$ and $7S_{1/2}$ states of several Tl isotopes. It is shown that the Gaussian basis set can be used in such electronic structure calculations and provide a good accuracy. For the ground electronic state of the neutral Tl atom achieved uncertainty for the hyperfine structure constant is smaller than 1\%. A strong Bohr-Weisskopf correction (about 16\%) was found for the $6P_{3/2}$ state which can be of interest for th…
In this paper we study the influence of electron screening on the Bohr-Weisskopf (BW) effect in many-electron atoms. The BW effect gives the finite-nucleus magnetization contribution to the hyperfine structure. Relativistic atomic many-body calculations are performed for s and p_1/2 states of several systems of interest for studies of atomic parity violation and time-reversal-violating electric dipole moments -- Rb, Cs, Fr, Ba+, Ra+, and Tl. For s states, electron screening effects are small, and the relative BW correction for hydrogenlike ions and neutral atoms is approximately the same. We r…
Constraints on new vector boson mediated electron-nucleus interactions from spectroscopy of polar diatomic molecules
Helmholtz Institut Mainz（亥姆霍兹研究所美因茨）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Institut für Physik, Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；University of California, Berkeley（加州大学伯克利分校）
The finite distribution of the nuclear magnetic moment across the nucleus gives a contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic Cs-133. This value is found from historical muonic-atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the precision heavy-atom comm…
Atomic electrons are sensitive to the properties of the nucleus they are bound to, such as nuclear mass, charge distribution, spin, magnetization distribution, or even excited level scheme. These nuclear parameters are reflected in the atomic transition energies. A very precise determination of atomic spectra may thus reveal information about the nucleus, otherwise hardly accessible via nuclear physics experiments. This work reviews theoretical and experimental aspects of the nuclear effects that can be identified in atomic structure data. An introduction to the theory of isotope shifts and hy…
