Bohr-Weisskopf Effect Research Articles

Precision hfs of 126Cs( [formula omitted]) by ABMR

The hfs separation Δ ν of 126Cs( T 1 / 2 = 1.63 m ) in the 6 s S 1 / 2 2 ground state was obtained in a precision measurement near zero magnetic field by means of atomic beam magnetic resonance with laser optical pumping on-line with the CERN-PSB-ISOLDE mass separator. The result, Δ ν = 3629.514 (0.001) MHz, corrects significantly a previous published value from a high-field experiment. With our result, the precision of the nuclear magnetic moment, μ ( Cs 126 ) ≈ 0.776 μ N , is now limited by the influence of extended nuclear structure on the hfs (the Bohr–Weisskopf effect).

Hyperfine splitting of hydrogenlike atoms based on relativistic mean field theory

We evaluate the hyperfine splitting of hydrogenlike $^{209}\mathrm{Bi}$ and $^{207}\mathrm{Pb}$ atoms based on a relativistic method for both the electron system and the nucleon system. The Bohr-Weisskopf (BW) effect is calculated with Lorentz covariant current. It is shown that the BW correction to the hyperfine splitting (HFS) is $0.58%--0.67%$ for $^{209}\mathrm{Bi}^{82+}$ and $3.79%--4.00%$ for $^{207}\mathrm{Pb}^{81+}$. It is also concluded that relativistic mean field theory reproduces the observed values of the HFS within the accuracy of $5%$ in $^{209}\mathrm{Bi}^{82+}$ and $13%$ in $^{207}\mathrm{Pb}^{81+}$.

Bohr–Weisskopf effect: influence of the distributed nuclear magnetization on hfs

Nuclear magnetic moments provide a sensitive test of nuclear wave functions, in particular those of neutrons, which are not readily obtainable from other nuclear data. These are taking added importance by recent proposals to study parity non-conservation (PNC) effects in alkali atoms in isotopic series. By taking ratios of the PNC effects in pairs of isotopes, uncertainties in the atomic wave functions are largely cancelled out at the cost of knowledge of the change in the neutron wave function. The Bohr–Weisskopf effect (B–W) in the hyperfine structure interaction of atoms measures the influence of the spatial distribution of the nuclear magnetization, and thereby provides an additional constraint on the determination of the neutron wave function. The added great importance of B–W in the determination of QED effects from the hfs in hydrogen-like ions of heavy elements, as measured recently at GSI, is noted. The B–W experiments require precision measurements of the hfs interactions and, independently, of the nuclear magnetic moments. A novel atomic beam magnetic resonance (ABMR) method, combining rf and laser excitation, has been developed for a systematic study and initially applied to stable isotopes. Difficulties in adapting the experiment to the ISOLDE radioactive ion beam, which have now been surmounted, are discussed. A first radioactive beam measurement for this study, the precision hfs of 126Cs, has been obtained recently. The result is 3629.515(∼0.001) MHz. The ability of ABMR to determine with high precision nuclear magnetic moments in free atoms is a desideratum for the extraction of QED effects from the hfs of the hydrogen-like ions. We also point out manifestations of B–W in condensed matter and atomic physics.

Hyperfine anomaly for the ground state of 9 Be

The Fermi contact parameter which represents hyperfine structure (hfs) has been accurately calculated for the ground state of the 9Be+ ion in a previous paper. In the present paper, the calculated parameter is compared with a high precision measurement to derive the hfs anomaly (the Bohr-Weisskopf effect), which is caused by nuclear magnetization distribution. The obtained hfs anomaly shows a satisfactory agreement with the result of a nuclear shell model calculation.

Relativistic many-body and QED effects on the hyperfine structure of lithium-like ions

The hyperfine splitting of the ground state of three-electron ions is studied in detail with the help of the multi-configuration Dirac-Fock method. We study the role of the magnetic electron-electron interaction and of the negative energy continuum. An all-order evaluation of some vacuum polarization corrections is performed. The Bohr-Weisskopf effect is evaluated in a simple model.

Hyperfine structure and \(\user1{g} \) factor measurements on Ba+ and Eu+ isotopes

Paul and Penning ion traps have been used to determine hyperfine structure coupling constants as well as nuclear \(\user1{g} \) factors of Ba+ ions with great precision. Attempts are under way to measure both quantities for a long chain of Eu isotopes in order to determine differential hyperfine anomalies for a better understanding of the Bohr–Weisskopf effect.

Calculation of the hyperfine structure of heavy H and Li like ions

The present status of calculations of the hyperfine splitting and the transition probability between the hyperfine splitting components in hydrogen and lithium like ions is discussed. The results of the calculations are compared with recent experimental data. A special attention is focused on the hyperfine splitting in hydrogen like lead and lithium like bismuth. It is shown that the theoretical prediction for the ground state hyperfine splitting in lead based on the single particle nuclear model for the Bohr-Weisskopf effect is in fair agreement with experiment. The theoretical prediction for the ground state hyperfine splitting in lithium like bismuth is improved due to more accurate calculations of the interelectronic interaction, QED, and nuclear corrections.

Nuclear magnetization distribution radii determined by hyperfine transitions in the1slevel of H-like ions185Re74+and187Re74+

The $F=3$ to $F=2$ hyperfine transitions in the $1s$ ground state of the two isotopes ${}^{185}{\mathrm{Re}}^{74+}$ and ${}^{187}{\mathrm{Re}}^{74+}$ were measured to be $(4560.5\ifmmode\pm\else\textpm\fi{}3)\AA{}$ and $(4516.9\ifmmode\pm\else\textpm\fi{}3)\AA{},$ respectively, using emission spectroscopy in an electron beam ion trap. After applying appropriate corrections for the nuclear charge distribution and QED effects, a Bohr-Weisskopf effect of \ensuremath{\varepsilon}=2.23(9)% and 2.30(9)% are found for ${}^{185}\mathrm{Re}$ and ${}^{187}\mathrm{R}\mathrm{e},$ respectively. This value is almost twice that of a previous theoretical estimate, and indicates a distribution of the nuclear magnetization far more extended than that of the nuclear charge. A radius of the magnetization distribution of $〈{r}_{m}^{2}{〉}^{1/2}=7.57(32)$ fm and $〈{r}_{m}^{2}{〉}^{1/2}$=7.69(32) fm for ${}^{185}\mathrm{Re}$ and ${}^{187}\mathrm{R}\mathrm{e},$ respectively, is inferred from the data. These radii are larger than the nuclear charge distribution radius $[〈{r}_{c}^{2}{〉}^{1/2}=5.39(1)$ fm] for both isotopes by factors 1.40(6) and 1.43(6), respectively. We find that the Bohr-Weisskopf effect in H-like ions is a sensitive probe of nuclear magnetization distribution, especially for cases where the charge distribution and magnetic moments are accurately known.

Some analytic results on the Uehling correction to hyperfine splitting in a muonic atom

We analyze the Uehling correction to the hyperfine structure of the ground state in hydrogenlike electronic and muonic atoms with a pointlike nucleus. The results are obtained analytically without any expansion over ~k. PACS No.: 31.20D Resume : Nous analysons la correction d’Uehling a la structure hyperfine du fondamental d’atomes hydrogenoides, electroniques ou muoniques, avec un noyau ponctuel, les resultats sont analytiques, sans recours a une expansion en puissances de ~k. [Traduit par la redaction] This work is a direct continuation of a previous paper [1] devoted to the Uehling correction to the Lamb shift (Fig. 1a) in a hydrogenlike atom with a pointlike nucleus. Here we calculate the spin-dependent part of the correction (Figs. 1b and 1c). In ref. 1, we examined the kind of integral for the complete Dirac wave function and the Uehling potential as a perturbation. More details will be found in a later paper1 where the method will be developed for any single-photon potential diagram including the one in Fig. 1b. The hyperfine structure (hfs) is more sensitive to the nuclear structure than the Lamb shift. As is well known, the theoretical uncertainty of the hyperfine splitting value for a hydrogenlike atom comes mainly from estimates of the nuclear magnetization distribution correction (the Bohr–Weisskopf effect). That is correct both for muonic and electronic atoms, but in the first case this correction is significantly larger and investigations of the hyperfine structure of muonic atoms can be used as a way to measure that effect and to apply the result to an electronic atom with the same nucleus. The hyperfine structure in a muonic atom being of the order +] ,p @ps is more important 1 S.G. Karshenboim. Manuscript in preparation. Received June 8, 1998. Accepted July 2, 1998. S.G. Karshenboim. D.I. Mendeleev Institute for Metrology, 198005 St. Petersburg, Russia. Telephone: 7-812-2591051; FAX: 7-812-1130114; e-mail: sgk@onti.vniim.spb.su V.G. Ivanov. Pulkovo Observatory, 196140, St. Petersburg, Russia. e-mail: ivanovv@gao.pnpi.spb.ru V.M. Shabaev. St. Petersburg State University, 198904, St. Petersburg, Russia. e-mail: shabaev@pobox.spbu.ru Can. J. Phys. 76: 503–506 (1998) © 1998 NRC Canada 504 Can. J. Phys. Vol. 76, 1998 Fig. 1. The Uehling corrections to the energy. The orbiting particle with mass 6 is either a muon or an electron and a particle in vacuum polarization loop is an electron.

Transition energy and lifetime for the ground-state hyperfine splitting of high-Zlithiumlike ions

The ground state hyperfine splitting values and the transition probabilities between the hyperfine structure components of high Z lithiumlike ions are calculated in the range $Z=49-83$. The relativistic, nuclear, QED and interelectronic interaction corrections are taken into account. It is found that the Bohr-Weisskopf effect can be eliminated in a combination of the hyperfine splitting values of the hydrogenlike and lithiumlike ions of an isotope. This gives a possibility for testing the QED effects in a combination of the strong electric and magnetic fields of the heavy nucleus. Using the experimental result for the $1s$ hyperfine splitting in ^{209}Bi^{82+}, the 2s hyperfine splitting in ^{209}Bi^{80+} is calculated to be \Delta E=0.7969(2) eV.

Ground-state hyperfine splitting of high-Zhydrogenlike ions

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 in ^{165}Ho^{66+} is in good agreement with experiment.

Ground-state hyperfine-structure measurements of unstableEu+isotopes in a Paul ion trap

Hyperfine separations in unstable ${\mathrm{Eu}}^{+}$ ions of mass 148, 149, and 150 have been measured in laser-microwave double-resonance experiments in a Paul ion trap. In spite of the small available quantities of the isotopes, the experimental uncertainties are of the order of ${10}^{\ensuremath{-}8}$ or below, which is of the same order as in earlier measurements on stable isotopes of ${\mathrm{Eu}}^{+}.$ Extensive second-order perturbation calculation is required to obtain coupling constants for magnetic-dipole $(A)$ and electric-quadrupole $(B)$ interactions. The uncertainties are a few times ${10}^{\ensuremath{-}7}$ for $A$ and ${10}^{\ensuremath{-}3}$ for $B.$ The experiments are a step in an attempt to determine the differential hyperfine anomaly (Bohr-Weisskopf effect) in a long chain of isotopes.

Atomic beam magnetic resonance apparatus for systematic measurement of hyperfine structure anomalies (Bohr-Weisskopf effect)

An atomic beam magnetic resonance (ABMR) apparatus has been constructed at Orsay, and has been installed at the CERN PS Booster ISOLDE mass separator facility for “on-line” work with radioactive isotopes in a program to measure hyperfine structure anomalies (the Bohr-Weisskopf effect) over long isotopic chains. The hfs anomalies result from the effect of the spatial distribution of the nuclear magnetization on the atomic hfs interaction. Constructional details of the system are described: emphasis is placed on the measurement of nuclear g-factors by a triple resonance, laser state selected, ABMR method. A precision better than 10 −4 for g I values has been obtained in stable atomic beam tests, leading to hfs anomaly measurements better than 10 percent. Two types of detection systems are described: laser fluorescence and surface ionization coupled with mass spectrometry.

Hyperfine structure andg-factor measurements in ion traps

We report about measurements on ground-state hyperfine splitting constants of stable Eu+ isotopes in radio frequency ion traps and experiments on the electronicg-factor of Ba+ in a Penning trap. From the precision of both measurements, which ranges between 3·10−6 and 5·10−7, we conclude that precise determination of the differential Bohr-Weisskopf effect in chains of isotopes will be possible in the near future.

Precision spectroscopy on trapped atomic ions

Recent examples of lifetime measurements, ground state hyperfine splittings and spectroscopy on minute samples of radioactive ions illustrate the extension of classical methods of spectroscopy to new regions of interest by the use of ion storage techniques. Estimates are given on the sensitivity of the method with respect to be possible investigation of the Bohr-Weisskopf effect in isotopic chains of elements.

Gyromagnetic ratios of the 4+ and 6+ rotational states of184W

The nuclear Larmor precession has been observed for the 2+, 4+ and 6+ rotational states of184W in the hyperfine field of WFe by application of the TDPAC and the IPAC techniques. A carrier free radioactive source of184mRe alloyed with high purity iron was used for all three measurements. From the Larmor precession observed in the 2+ state by TDPACω L = 944(15) MHz and the knowng-factor the hyperfine fieldB 300 K hf (WFe)=−69.6(27)T was derived. The deviation from the result of a spin echo experiment with183WFe extrapolated to room temperature may be caused by the Bohr-Weisskopf effect (hyperfine anomaly). IPAC measurements with the same sample polarized in an external magnetic field of 1.6T gave for the 4+ and 6+ rotational states: ω L τ(4+)=0.0609(22) andω L τ(6+)=0.00735(102). By use of experimentalB(E2)-values theg R -factors were derived asg R (4+)=+0.276(26) andg R (6+)=+0.281(45). The directional correlation of the 537−384 keVγ-γ cascade has been analysed in terms of anE1/M2/E3 mixture for theK-forbidden 537keV transition. We obtained the mixing ratiosδ(M2/E1)=±0.086(16),δ(E3/E1)=−0.028(5) with the sign convention of Krane and Steffen.

Hyperfine structure of μ-mesic atoms

The effects of the distribution of nuclear magnetization on hyperfine structure (Bohr-Weisskopf effect) are studied in the case of μ-mesic atoms. The “configuration mixing” model of the nucleus is used for the calculation and it is shown that the reduction of hyperfine structure is of the order of 15% for Al 27 and of 50% for Bi 209. Calculations are also made in the framework of the collective model for Al 27 and for Ta 181. The vacuum polarization effects on hyperfine structure are studied and are found to be of the order of 1% for light nuclei.

Configuration Mixing and the Effects of Distributed Nuclear Magnetization on Hyperfine Structure in Odd-ANuclei

The theory of Blin-Stoyle and of Arima and Horie, in which the deviations of the nuclear magnetic moments from the single-particle model Schmidt limits are ascribed to configuration mixing, is used as a model to account quantitatively for the effects of the distribution of nuclear magnetization on hyperfine structure (Bohr-Weisskopf effect). A diffuse nuclear charge distribution, as approximated by the trapezoidal Hofstadter model, is used to calculate the required radial electron wave functions. A table of single-particle matrix elements of ${R}^{2}$ and ${R}^{4}$ in a Saxon-Woods type of potential well is included. Explicit formulas are derived to permit comparison with experiment. For all of the available data satisfactory agreement is found. The possibility of using hyperfine structure measurements sensitive to the distribution of nuclear magnetization in a semiphenomenological treatment in order to obtain information on nuclear configurations is indicated.