Bohr-Weisskopf Effect Research Articles

Calculation of the Differential Breit-Rosenthal Effect in Pb

Recent advancements in studying long chains of unstable nuclei have revitalised interest in investigating the hyperfine anomaly. Hyperfine anomaly is particularly relevant for determining nuclear magnetic dipole moments using hyperfine structures where it limits the accuracy. This research paper focuses on the calculation of the differential Breit-Rosenthal effect for the 6p23P1,2, 1D2 and 6p7s3P1 states in Pb, utilising the multi-configurational Dirac-Hartree-Fock code, GRASP2018. The findings show that the differential Breit-Rosenthal effect is typically less than 0.1/fm2, which is often much smaller than the Bohr-Weisskopf effect. The differential Breit-Rosenthal effect for the 6p23P2 state is one order of magnitude smaller than the rest, which is why this state seems to be insensible to the hyperfine anomaly.

Empirical Determination of the Bohr-Weisskopf Effect in Cesium and Improved Tests of Precision Atomic Theory in Searches for New Physics.

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 ^{133}Cs. 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 community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

Bohr-Weisskopf effect: From hydrogenlike-ion experiments to heavy-atom calculations of the hyperfine structure

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 relate the ground-state BW effect in H-like ions, which may be cleanly extracted from experiments, to the BW effect in s and p_1/2 states of neutral and near neutral atoms through an electronic screening factor. This allows the BW effect extracted from measurements with H-like ions to be used, with screening factors, in atomic calculations without recourse to modelled nuclear structure input. It opens the way for unprecedented accuracy in accounting for the BW effect in heavy atoms. The efficacy of this approach is demonstrated using available experimental data for H-like and neutral Tl-203 and Tl-205.

Precision Calculation of Hyperfine Constants for Extracting Nuclear Moments of ^{229}Th.

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 a 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 ^{229}Th^{3+} in the framework of such a relativistic coupled-cluster single double triple method. We present a detailed study of various corrections to all calculated properties. Using the theory results and experimental data, we found the nuclear magnetic dipole and electric quadrupole moments to be μ=0.366(6)μ_{N} and Q=3.11(2) eb, respectively, and reduce the uncertainty of the quadrupole moment by a factor of 3. The Bohr-Weisskopf effect of the finite nuclear magnetization is investigated, with bounds placed on the deviation of the magnetization distribution from the uniform one.

Comparison of Methods for Eliminating the Bohr–Weisskopf Effect in Atomic Spectra of $${}^{{209}}$$Bi Heavy Ions

Comparison of Methods for Eliminating the Bohr–Weisskopf Effect in Atomic Spectra of $${}^{{209}}$$Bi Heavy Ions

The Bohr–Weisskopf Effect in the Atomic Spectra of Heavy Ions of 209Bi

Two ways of eliminating the Bohr–Weisskopf effect in the theory of hyperfine splitting (HFS) are compared: the ratio and specific-difference (SD) approaches to the differences between the HFS values in different shells. A comparison reveals a number of disadvantages in the SD approach. Conclusions based on results obtained in regard to further refining the magnetic moment of the 209Bi nucleus with heavy ions in the storage rings of GSI Darmstadt and IMP Lanzhou are considered.

Calculation of the Differential Breit–Rosenthal Effect in the 6s6p 3P1,2 States of Hg

Studies of the hyperfine anomaly has found a renewed interest with the recent development of techniques to study the properties of long chains of unstable nuclei. By using the hyperfine structure for determining the nuclear magnetic dipole moments, the hyperfine anomaly puts a limit to the accuracy. In this paper, the differential Breit–Rosenthal effect is calculated for the 6s6p3P1,2 states in 199Hg as a function of the change in nuclear radii, using the MCDHF code, GRASP2018. The differential Breit–Rosenthal effect was found to be of the order of 0.1%fm−2, in most cases much less than the Bohr-Weisskopf effect. The results also indicate that large calculations might not be necessary, with the present accuracy of the experimental values for the hyperfine anomaly.

Nuclear magnetization distribution effect in molecules: Ra+ and RaF hyperfine structure.

Recently, the first laser spectroscopy measurement of the radioactive RaF molecule has been reported by Ruiz et al. [Nature 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 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 225Ra+ cation and 225RaF molecule. For the ground state of the 225RaF molecule, this contribution achieves 4%.

Nuclear Magnetic Moments of Francium-207-213 from Precision Hyperfine Comparisons.

We report a fourfold improvement in the determination of nuclear magnetic moments for neutron-deficient francium isotopes 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 accuracy. An improved understanding of the nuclear magnetic moments and Bohr-Weisskopf effect are crucial for benchmarking the atomic theory required in precision tests of the standard model, in particular atomic parity violation studies, that are underway in francium.

Hyperfine Anomaly in Eu Isotopes and the Universiability of the Moskowitz–Lombardi Formula

A method for determining the hyperfine anomaly, without using the nuclear magnetic moments, is used on a series of unstable isotopes of Eu. The large number of experimental data in Eu makes it possible to extract the hyperfine anomaly for a number of unstable isotopes. Calculations of the Bohr–Weisskopf effect and hence the hyperfine anomaly are performed using the particle-rotor formalism. The result from the calculations and experiments is compared with other theoretical calculations and the empirical Moskowitz–Lombardi formula. The results show that the Moskowitz–Lombardi formula is not universal.

Examination of the solution to the hyperfine structure “puzzle” in H-like and Li-like Bi209 ions

Some aspects of description of the Bohr-Weisskopf effect in hyperfine splitting of the H- and Li-like ions of 209Bi are considered by application of the surface and volume models of the nuclear currents. Extension of these models, used in internal conversion theory, to description of the HFS allows one to successfully describe the effect, without resorting to the specific differences. The latters are shown not to be needed at all. Moreover, they turn out to depend on the nuclear model even stronger than the HFS values themselves. Comparison of the calculated HFS values to experiment shows a satisfactory agreement. Both models provide equally good description of the effect. However, they result in different values of the retrieved rms radius of the nuclear magnetization. In this respect, situation resembles the proton radius puzzle. Prospects of future research are discussed.

Anomalous Internal Conversion as a Clue to Solving the 209Bi Puzzle

Theory of anomalous internal conversion is developed, and extended for the description of the hyperfine splitting. Experimental data on the hyperfine splitting in the H- and Li-like heavy ions of 209Bi are analyzed in terms of the Bohr-Weisskopf effect. Agreement with the theory is achieved, scheduling light on the structure of the magnetization distribution over the nuclear volume.

Magnetic hyperfine structure of the ground-state doublet in highly charged ionsTh89+,87+229and the Bohr-Weisskopf effect

The magnetic hyperfine (MHF) structure of the $5/2^+$(0.0 eV) ground state and the low-lying $3/2^+$(7.8 eV) isomeric state of the $^{229}$Th nucleus in highly charged ions Th$^{89+}$ and Th$^{87+}$ is calculated. The distribution of the nuclear magnetization (the Bohr-Weisskopf effect) is accounted for in the framework of the collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. The deviations of the MHF structure for the ground and isomeric states from their values in the model of point-like nuclear magnetic dipole are calculated. The influence of the mixing of the states with the same quantum number $F$ on the energy of sublevels is studied. Taking into account the mixing of states, the probabilities of the transitions between the components of MHF structure are found.

Hyperfine Anomalies in Fr: Boundaries of the Spherical Single Particle Model

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 neutron-deficient isotopes (^{207-213}Fr). Also, we find near-constant proton anomalies for several even-N isotopes. This identifies a set of Fr isotopes whose nuclear structure can be understood well enough for the extraction of weak interaction parameters from parity nonconservation studies.

The theory of the Bohr–Weisskopf effect in the hyperfine structure

Description of the Bohr–Wesskopf effect in the hyperfine structure of few-electron heavy ions is a challenging problem, which can be used as a test of both QED and atomic calculations. However, for twenty years the research has actually been going in a wrong direction, aimed at fighting the Bohr–Weisskopf effect through its cancellation in specific differences. Alternatively, we propose the constructive model-independent way, which enables the nuclear radii and their momenta to be retrieved from the hyper-fine splitting (HFS). 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. It is shown that the parameters which can be extracted from the data are the even nuclear momenta of the magnetization distribution. The radii R2 and – for the first time – R4 are obtained in this way by analysis of the experimental HFS values for the H- and Li-like ions of 209Bi. The critical prediction concerning the HFS for the 2p12 state is made. The present analysis shows high sensitivity of the method to the QED effects, which offers a way of precision test of QED. Experimental recommendations are given, which are aimed at retrieving data on the HFS values for a set of a few-electron configurations of each atom.

Hyperfine structure constant of the neutron halo nucleus (11)Be(+).

The hyperfine splittings of ground state Be+11 have been measured precisely by laser-microwave double resonance spectroscopy for trapped and laser cooled beryllium ions. The ions were produced at relativistic energies and subsequently slowed down and trapped at mK temperatures. The magnetic hyperfine structure constant of Be+11 was determined to be A11=-2677.302 988(72) MHz from the measurements of the mF-mF'=0-0 field independent transition. This measurement provides essential data for the study of the distribution of the halo neutron in the single neutron halo nucleus Be11 through the Bohr-Weisskopf effect.

Measurement of the hyperfine splitting of the6S1/2level in rubidium

We present a measurement of the hyperfine splitting of the 6S$_{1/2}$ excited level of rubidium using two photon absorption spectroscopy in a glass cell. The values we obtain for the magnetic dipole constant A are 239.18(03) MHz and 807.66(08) MHz for $^{85}$Rb and $^{87}$Rb, respectively. The combination of the magnetic moments of the two isotopes and our measurements show a hyperfine anomaly in this atomic excited state. The observed hyperfine anomaly difference has a value of $_{87}\delta_{85}=-0.0036(2)$ due to the finite distribution of nuclear magnetization, the Bohr-Weisskopf effect.

Comparison of hyperfine anomalies in the [formula omitted] and [formula omitted] levels of 85Rb and 87Rb

We observe a hyperfine anomaly in the measurement of the hyperfine splitting of the 6S1/2 excited level in rubidium. We perform two step spectroscopy using the 5S1/2→5P1/2→6S1/2 excitation sequence. We measure the splitting of the 6S1/2 level and obtain for the magnetic dipole constants of 85Rb and 87Rb A=239.18(4)MHz and A=807.66(8)MHz, respectively. The hyperfine anomaly difference of δ8587=−0.0036(2) comes from the Bohr Weisskopf effect: a correction to the point interaction between the finite nuclear magnetization and the electrons, and agrees with that obtained in the 5S1/2 ground state.

Calculations of the Hyperfine Anomaly in the Lanthanides

Calculations of the Bohr-Weisskopf effect and hence the hyperfine anomaly has been performed in Eu using the particle-rotor formalism. Comparisons with experimental data and a discussion on the semi-empirical Moskowitz-Lombardi formula is performed.

The hyperfine structure of heavy hydrogen-like ions: Calculation based on experimental data on muonic atoms

A procedure for the calculation of the correction to the hyperfine structure of hydrogen-like ions for the Bohr-Weisskopf effect is developed on the basis of experimental data on muonic atoms. The calculations take into account the quantum electrodynamic corrections both for muonic atoms and for electronic ions. The single-particle model and the configuration mixing model of the nucleus are considered. The results of the calculations are compared with known theoretical and experimental data.