Electric Quadrupole Hyperfine Structure Constants Research Articles

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.

Laser spectroscopy of indium Rydberg atom bunches by electric field ionization

This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over previous non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions in the indium atom from the text {5s}^2text {5d},^2text {D}_{5/2} and text {5s}^2text {5d},^2text {D}_{3/2} states to text {5s}^2np ^2P and text {5s}^2ntext {f},^2F Rydberg states, up to a principal quantum number of n=72. The extracted Rydberg level energies were used to re-evaluate the ionization potential of the indium atom to be 46,670.107(4),hbox {cm}^{-1}. The nuclear magnetic dipole and nuclear electric quadrupole hyperfine structure constants and level isotope shifts of the text {5s}^2text {5d},^2text {D}_{5/2} and text {5s}^2text {5d},^2text {D}_{3/2} states were determined for ^{113,115}In. The results are compared to calculations using relativistic coupled-cluster theory. A good agreement is found with the ionization potential and isotope shifts, while disagreement of hyperfine structure constants indicates an increased importance of electron correlations in these excited atomic states. With the aim of further increasing the detection sensitivity for measurements on exotic isotopes, a systematic study of the field-ionization arrangement implemented in the work was performed at the same time and an improved design was simulated and is presented. The improved design offers increased background suppression independent of the distance from field ionization to ion detection.

Laser spectroscopic investigation of atomic holmium in the wavelength range from 780 nm to 830 nm: Hyperfine structure measurements and a new energy level

The hyperfine structure of neutral holmium was studied using a hollow cathode discharge lamp and laser-induced fluorescence spectroscopy or optogalvanic spectroscopy, respectively. Altogether 42 spectral lines in the wavelength range from 780 nm to 830 nm were investigated. Magnetic dipole hyperfine structure constants A and electric quadrupole hyperfine structure constants B were determined for 23 levels of even parity and for 25 levels of odd parity. Eight of the reported hyperfine structure constants have not been published before. For most other levels, previously published hyperfine structure constants have been measured with greater precision. Additionally, one new energy level 29013.43 cm−1 with odd parity and J=13/2 has been discovered.

Calculations of the atomic structure for the low-lying states of actinium

We employ a technique that combines the configuration interaction method with the singles-doubles coupled-cluster method to perform calculation of the energy levels, transition amplitudes, lifetimes, g-factors, and magnetic dipole and electric quadrupole hyperfine structure constants for many low-lying states of neutral actinium. We find very good agreement with existing experimental energy levels and make accurate predictions for missing levels. It has been noted that some of the levels have been previously misidentified; our analysis supports this claim. If spectroscopy is performed with actinium-225, our calculations will lead to values for nuclear structure constants. The accuracy of this can be constrained by comparing with actinium-227.

Hyperfine structure measurements of neutral vanadium by inter-modulated laser-induced fluorescence spectroscopy in the wavelength range from 800 nm to 830 nm

The hyperfine structure of eight spectral lines of neutral vanadium is investigated by Doppler-reduced inter-modulated laser-induced fluorescence spectroscopy using a Ti-Sa laser in the wavelength range from 800 nm to 830 nm. The spectra are compared with previous measurements with Doppler-limited laser-induced fluorescence spectroscopy. Improved and revised magnetic dipole hyperfine structure constants A are presented for five levels as well as new electric quadrupole hyperfine structure constants B for two levels.

Ab initio calculations of the hyperfine structure of zinc and evaluation of the nuclear quadrupole moment Q(Zn67)

The relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and the non-relativistic multiconfiguration Hartree-Fock (MCHF) methods have been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants of zinc. The calculated electric field gradients for the $ 4s 4p \,\, ^3 \! P^o_{1} $ and $ 4s 4p \,\, ^3 \! P^o_{2} $ states, together with experimental values of the electric quadrupole hyperfine structure constants, made it possible to extract a nuclear electric quadrupole moment $ Q(^{67}{\rm Zn}) = 0.122(10) $ b. The error bar has been evaluated in a quasi-statistical approach - the calculations had been carried out with eleven different methods, and then the error bar has been estimated from the differences between the results obtained with those methods.

Diverse trends of electron correlation effects for properties with different radial and angular factors in an atomic system: a case study in Ca+

Dependencies of electron correlation effects with the rank and radial behavior of spectroscopic properties are analyzed in the singly charged calcium ion (Ca+). To demonstrate these trends, we have determined field shift constants, magnetic dipole and electric quadrupole hyperfine structure constants, Landé gJ factors, and electric quadrupole moments that are described by electronic operators with different radial and angular factors. Radial dependencies are investigated by comparing correlation trends among the properties that have similar angular factors and vice versa. To highlight these observations, we present results from the mean-field approach to all-orders along with intermediate contributions. Contributions from higher relativistic corrections are also given. These findings suggest that sometime lower-order approximations can give results agreeing with the experimental results, but inclusion of some of higher-order correlation effects can cause large disagreement with the experimental values. Therefore, validity of a method for accurate evaluation of atomic properties can be tested by performing calculations of several properties simultaneously that have diverse dependencies on the angular and radial factors and comparing with the available experimental results. Nevertheless, it is imperative to include full triple and quadrupole excitations in the all-order many-body methods for high-precision calculations that are yet to be developed adopting spherical coordinate system for atomic studies.

Hyperfine structure measurements of neutral vanadium by laser-induced fluorescence spectroscopy in the wavelength range from 750 nm to 860 nm

The hyperfine structure of 57 spectral lines of neutral vanadium has been investigated using a hollow cathode lamp by laser-induced fluorescence spectroscopy in the wavelength range from 750 nm to 860 nm. New magnetic dipole hyperfine structure constants A have been determined for 14 atomic energy levels and new electric quadrupole hyperfine structure constants B for two levels. Additionally previously published hyperfine structure constants A of 56 levels have been measured again. In five cases, the old A values have been rejected and replaced by improved values.

Fine- and hyperfine structure investigations of even configuration system of atomic terbium

In this work a parametric study of the fine structure (fs) and the hyperfine structure (hfs) for the even-parity configurations of atomic terbium (Tb I) is presented, based in considerable part on the new experimental results. Measurements on 134 spectral lines were performed by laser induced fluorescence (LIF) in a hollow cathode discharge lamp; on this basis, the hyperfine structure constants A and B were determined for 52 even-parity levels belonging to the configurations 4f85d6s2, 4f85d26s or 4f96s6p; in all the cases those levels were involved in the transitions investigated as the lower levels. For 40 levels the hfs was examined for the first time, and for the remaining 12 levels the new measurements supplement our earlier results. As a by-product, also preliminary values of the hfs constants for 84 odd-parity levels were determined (the investigations of the odd-parity levels system in the terbium atom are still in progress). This huge amount of new experimental data, supplemented by our earlier published results, were considered for the fine and hyperfine structure analysis. A multi-configuration fit of 7 configurations was performed, taking into account second-order of perturbation theory, including the effects of closed shell-open shell excitations. Predicted values of the level energies, as well as of magnetic dipole and electric quadrupole hyperfine structure constants A and B, are quoted in cases when no experimental values are available. By combining our experimental data with our own semi-empirical procedure it was possible to identify correctly the lower and upper level of the line 544.1440nm measured by Childs with the use of the atomic-beam laser-rf double-resonance technique (Childs, J Opt Soc Am B 9;1992:191–6).

Extended analysis of the system of even configurations of Ta II

We performed a parametric study of the fine (fs) and hyperfine structure (hfs) for the even parity configurations of ionized tantalum (Ta II) using improved experimental fs and hfs data for 88 levels. A multi-configuration fitting procedure was performed for 47 configurations taking into account second-order perturbation theory including the effects of closed to open shell excitations. The fs and hfs parameters were calculated. Predicted values of level energies up to 86000cm−1 are given, as well as gJ-Landé factors, magnetic dipole and electric quadrupole hyperfine structure constants A and B, when no experimental values are available.

Hyperfine structure and lifetime measurements in the 4s2nd 2D3/2 Rydberg sequence of Ga I by time-resolved laser spectroscopy

The hyperfine structure (HFS) constants of the 4s2nd 2D3/2 (n=6–18) Rydberg sequence and the 4s26p 2P3/2 level for two isotopes of 69Ga and 71Ga atoms were measured by means of the time-resolved laser-induced fluorescence (TR-LIF) technique and the quantum beat method. The observed hyperfine quantum beat spectra were analyzed and the magnetic-dipole HFS constants A as well as the electric-quadrupole HFS constants B of these levels were obtained by Fourier transform and a program for multiple regression analysis. Also using TR-LIF method radiative lifetimes of the above sequence states were determined at room temperature. The measured lifetime values range from 69 to 2279ns with uncertainties no more than 10%. To our knowledge, the HFS constants of this Rydberg sequence and the lifetimes of the 4s2nd 2D3/2 (n=10–18) levels are reported for the first time. Good agreement between our results and the previous is achieved.

Measurement of absolute frequencies and hyperfine structure constants of4D5/2and4D3/2levels ofRb87andRb85using an optical frequency comb

We report the absolute frequency values of all (ten) hyperfine transitions of $5{P}_{3/2}\ensuremath{-}4{D}_{5/2}$ and $5{P}_{3/2}\ensuremath{-}4{D}_{3/2}$ for $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$ atoms via the use of an optical frequency comb by measuring the frequency of a laser diode stabilized onto the line centers of the double-resonance optical pumping spectra. Here we report on the absolute frequencies for the two transitions $[{}^{85}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}5{P}_{3/2}({F}^{\ensuremath{'}}=4)\ensuremath{-}4{D}_{5/2}\phantom{\rule{0.16em}{0ex}}({F}^{\ensuremath{'}\ensuremath{'}}=3,4)]$. Furthermore, the frequency uncertainties are reduced significantly for the other transitions. Moreover, the magnetic dipole and the electric quadrupole hyperfine structure constants of $4{D}_{5/2}$ for $^{87}\mathrm{Rb}$ and $^{85}\mathrm{Rb}$ are determined by using the measured values of the absolute frequency.

CI-MBPT: A package of programs for relativistic atomic calculations based on a method combining configuration interaction and many-body perturbation theory

This package of programs allows us to carry out relativistic calculations for many-electron atoms and ions. One can find energy levels and a number of atomic properties: g-factors, magnetic-dipole and electric-quadrupole hyperfine structure constants, electric- and magnetic-multipole transition amplitudes, and matrix elements of the parity nonconserving interactions. Method of calculation is based on a combination of conventional configuration interaction (CI) method and many-body perturbation theory (MBPT). The former explicitly accounts for the interaction between valence electrons, while the latter includes core–core and core–valence correlations. These two methods are combined to acquire benefits from both approaches and attain better accuracy. Program summaryProgram title: CI-MBPTCatalogue identifier: AEWV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 102640No. of bytes in distributed program, including test data, etc.: 583539Distribution format: tar.gzProgramming language:Fortran 90.Computer: Intel Core i5 CPU, 3.2 GHz.Operating system: Linux (CentOS 5, Ubuntu 12.04 LTS, SUSE 13.2).RAM: 8 GbClassification: 2.1.Nature of problem: Prediction of atomic or ionic energy levels and different observables in the framework of relativistic approach.Solution method: The package of programs determines energy levels and associated many-electron wave functions for states of atoms and ions in the pure CI or CI+MBPT approximations. Using the wave functions, different atomic properties can be obtained, including g-factors, magnetic-dipole and electric-quadrupole hyperfine structure constants, electric- and magnetic-multipole transition amplitudes, P-odd and P,T-odd amplitudes.Restrictions: The package is not designed for calculations of high Rydberg and autoionizing states. It becomes inefficient for the number of valence electrons exceeding four or five. It has not been tested for superheavy elements. The maximal number of Hartree–Fock–Dirac (HFD) orbitals when HFD equations are solved is 32.Unusual features: One-electron orbitals outside the nucleus are defined on radial grid points. Inside the nucleus they are described in a form of the Taylor expansion over r/R, where R is the nuclear radius.Additional comments: All programs have been compiled, linked, and tested with both “ifort” and freely available “gfortran”.Running time: Changes from tens of minutes for atoms with two valence electrons to tens of hours for more complex systems.

Hyperfine structure near infrared spectrum of atomic iodine

The hyperfine structure of spectral lines of neutral iodine (II) in the wavenumber region from 11300cm−1 to 13000cm−1 was studied using optical heterodyne concentration modulation absorption spectroscopy with a tunable single-mode cw Ti:Sapphire laser. The iodine atoms were produced and excited by a discharge operated in a mixture of helium and iodine vapor. A total of 89 lines were observed and the hyperfine structure of 45 of these lines was studied. For 40 lines, the hyperfine structure was not previously known. The magnetic dipole and the electric quadrupole hyperfine structure constants of 18 even and 28 odd levels were extracted. The constants of one even level and of 16 odd levels are presented for the first time.

Correlation trends in the hyperfine structures ofFr210,212

We demonstrate the importance of electron correlation effects in the hyperfine structure constants of many low-lying states in $^{210}\mathrm{Fr}$ and $^{212}\mathrm{Fr}$. This is achieved by calculating the magnetic dipole and electric quadrupole hyperfine structure constants using the Dirac-Fock approximation, second-order many-body perturbation theory, and the coupled-cluster method in the singles and doubles approximation in the relativistic framework. By combining our recommended theoretical results with the corresponding experimental values, improved nuclear magnetic dipole and electric quadrupole moments of the above isotopes are determined. In the present work, it is observed that there are large discrepancies between the hyperfine structure constants of the $7{D}_{5/2}$ state obtained from the experimental and theoretical studies, whereas good agreement is found for the other ${D}_{5/2}$ states. Our estimated hyperfine constants for the $8P,\phantom{\rule{0.16em}{0ex}}6D,\phantom{\rule{0.16em}{0ex}}10S$, and $11S$ states could be very useful as benchmarks for the measurement of these quantities.

Spectral properties of a few F-like ions

Aims. We intend to provide accurate data for the oscillator strengths, transition probabilities, lifetimes, and hyperfine shifts of the atomic energy levels in the fluorine (F)- like Ti, V, Cr, Mn, Co, Ni, Cu, Zn, and Mo ions for the diagnostic of the astrophysical plasma. Furthermore, we propose these ions for probing possible variation in the fine structure constant (αe) by observing their transition lines from the distant astronomical objects. Methods. We have employed an all-order perturbative method in the relativistic coupled-cluster framework using the Dirac-Coulomb Hamiltonian for calculating the atomic wave functions in the considered F-like ions. We adopted the Fock-space formalism to account for the correlation effects among the occupied electrons by allowing all possible singly and doubly excited configurations in two steps: first considering the correlations between the electrons in a closed-shell configuration, and second constructing the openshell configurations of the first three low-lying states in the considered atomic systems by removing the respective electron from the core orbitals. This procedure enormously simplifies the computational complexity and overcomes the need to select important configuration state functions in determining the atomic state functions in contrast to a truncated configuration interaction method. Moreover, corrections from the frequency-independent Breit interaction and the lowest order quantum electrodynamic effects are incorporated self-consistently. Results. We present the calculated ionization potential energies of the electrons that are detached to form the above considered F-like ions. The correctness of our estimated results are ensured by comparing them with the available experimental values and other calculations. From these calculations, we evaluate the relativistic sensitivity coefficients that we propose here to be used for probing possible temporal variation of the fine structure constant (αe) through the precise astrophysical observation of the spectral lines of the transitions involving the above low-lying states. The accuracies of these sensitivity coefficients are appraised from the comparison of our calculated energies with the experimental values. We also present the line strengths by calculating the reduced matrix elements of the allowed transitions and of the M1 and E2 forbidden transitions. By combining our calculated line strengths with the observed wavelengths, we determine the oscillator strengths, transition probabilities, and lifetimes of the first two excited states of the above ions and compare them with the other theoretical calculations. The hyperfine splittings of the states are also presented by calculating their magnetic dipole and electric quadrupole hyperfine structure constants.

Hyperfine structure investigations of atomic niobium with optogalvanic and laser-induced fluorescence spectroscopy in the near-infrared wavelength range

Aims. The aim of this work is to increase the amount of hyperfine structure data of atomic niobium (Nb I), which is needed for astrophysicists for the detailed analysis of new stellar spectra. Particular emphasis was placed on the investigation of energy levels with unknown hyperfine structure constants. Methods. The hyperfine structure in the spectrum of Nb I was studied using laser-induced fluorescence spectroscopy and laser optogalvanic spectroscopy with a tuneable single-mode cw Ti:Sa laser in the wavelength range from 750 nm to 865 nm. The Nb atoms were produced and excited in a liquid-nitrogen-cooled hollow-cathode plasma. Results. We measured and analysed 81 spectral lines, 19 of which are not previously known from the literature. In total, the magnetic dipole hyperfine structure constants A were determined for 28 energy levels of even and 53 energy levels of odd parity. The electric quadrupole hyperfine structure constants B were only determined in a few cases, when the spectra were clearly resolved and/or when a level was found from several transitions. The magnetic dipole hyperfine structure constants A of 13 even and 11 odd levels as well as the electric quadrupole hyperfine structure constants B of 13 even and 17 odd levels are presented for the first time. For the other levels, improved values of hyperfine structure constants are given. Conclusions. The hyperfine structure can have a significant effect on stellar absorption line profiles, and the corresponding abundances can be substantially overestimated if these effects are not taken into account. Therefore, a detailed consideration of the hyperfine structure is important for stellar abundance determinations. The present work substantially increases the knowledge of hyperfine structure of Nb, which plays an important role in investigating the nucleosynthesis of heavy elements.

Fock-space relativistic coupled-cluster calculations of two-valence atoms

We have developed an all-particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine structure constants, and electric dipole matrix elements of Sr, Ba, and Yb. Furthermore, we calculate the electric quadrupole hyperfine structure constants and the electric dipole matrix elements of ${\mathrm{Sr}}^{+}$, ${\mathrm{Ba}}^{+}$, and ${\mathrm{Yb}}^{+}$. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine structure constants of ${\mathrm{Yb}}^{+}$.

Complete-active-space multiconfiguration Dirac-Hartree-Fock calculations of hyperfine-structure constants of the gold atom

The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the expectation values for the hyperfine splittings of the 5d96s2 2D3/2 and 5d96s2 2D5/2 levels of atomic gold. One-, two-, and three-body electron correlation effects involving all 79 electrons have been included in a systematic manner. The approximation employed in this study is equivalent to a Complete Active Space (CAS) approach. Calculated electric field gradients, together with experimental values of the electric quadrupole hyperfine structure constants, allow us to extract a nuclear electric quadrupole moment Q(197Au)=521.5(5.0) mb.

High resolution measurements of the hyperfine structure of atomic Lanthanum for energetically low lying levels of odd parity

Doppler-reduced saturation absorption spectroscopy is applied to study the hyperfine structure of excited levels of Lanthanum. 16 transitions in the near infrared wavelength range are investigated. Precise values for the magnetic dipole hyperfine structure constants A as well as for the electric quadrupole hyperfine structure constants B of the isotope 139La are determined for 14 levels of odd parity and nine levels of even parity. For levels of even parity a good agreement is found with values from previous measurements using sub-Doppler methods. For levels of odd parity previously determined values are improved and for two levels new values of the hyperfine structure constants are reported.