Magnetic Dipole Hyperfine Structure Constants Research Articles

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.

HYPERFINE STRUCTURE CONSTANTS OF ENERGETICALLY HIGH-LYING LEVELS OF ODD PARITY OF ATOMIC VANADIUM

High-resolution Fourier transform spectra of a vanadium-argon plasma have been recorded in the wavelength range of 365-670 nm (15,000-27,400 cm–1). Optical bandpass filters were used in the experimental setup to enhance the sensitivity of the Fourier transform spectrometer. In total, 138 atomic vanadium spectral lines showing resolved or partially resolved hyperfine structure have been analyzed to determine the magnetic dipole hyperfine structure constants A of the involved energy levels. One of the investigated lines has not been previously classified. As a result, the magnetic dipole hyperfine structure constants A for 90 energy levels are presented: 35 of them belong to the configuration 3d 34s4p and 55 to the configuration 3d 44p. Of these 90 constants, 67 have been determined for the first time, with 23 corresponding to the configuration 3d 34s4p and 44 to 3d 44p.

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.

Relativistic effects on the hyperfine structures of2p4(3P)3p2Do,4Do, and4Poin19F i

The hyperfine interaction constants of the 2p4(3P)3p 2Do_{3/2,5/2}, 4Do_{1/2-7/2} and 4Po_{1/2-5/2} levels in neutral fluorine are investigated theoretically. Large-scale calculations are carried out using the multiconfiguration Hartree-Fock (MCHF) and Dirac-Hartree-Fock (MCDHF) methods. In the framework of the MCHF approach, the relativistic effects are taken into account in the Breit-Pauli approximation using non relativistic orbitals. In the fully relativistic approach, the orbitals are optimized using the Dirac-Coulomb Hamiltonian with correlation models inspired by the non relativistic calculations. Higher-order excitations are captured through multireference configuration interaction calculations including the Breit interaction. In a third (intermediate) approach, the Dirac-Coulomb-Breit Hamiltonian matrix is diagonalized in a relativistic configuration space built with non relativistic MCHF radial functions converted into Dirac spinors using the Pauli approximation. The magnetic dipole hyperfine structure constants calculated with the three relativistic models are consistent and reveal unexpectedly large effects of relativity for 2Do_{5/2}, 4Po_{3/2} and 4Po_{5/2}. The agreement with the few available experimental values is satisfactory. The strong J-dependence of relativistic corrections on the hyperfine constants is investigated through the detailed analysis of the orbital, spin-dipole and contact relative contributions calculated with the non relativistic magnetic dipole operator.

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.

Reexamination of nuclear quadrupole moments in39−41K isotopes

Nuclear quadrupole moments ($Q$'s) in three isotopes of the potassium atom (K) with mass numbers 39, 40, and 41 are evaluated more precisely in this work. The $Q$ value of ${}^{39}$K is determined to be 0.0614(6) $b$ by combining the available experimental result of the electric quadrupole hyperfine structure constant ($B$) with our calculated $B/Q$ result of its $4{P}_{3/2}$ state. Furthermore, combining this $Q$ value with the measured ratios $Q$(${}^{40}$K)$/Q$(${}^{39}$K) and $Q$(${}^{41}$K)$/Q$(${}^{39}$K), we obtain $Q$(${}^{40}$K)$=\ensuremath{-}0.0764(8)\phantom{\rule{4pt}{0ex}}b$ and $Q$(${}^{41}$K)$=0.0747(7)\phantom{\rule{4pt}{0ex}}b$, respectively. These results disagree with the sub-1$%$ accuracy standard values recently quoted by Pyykk\"o [Mol. Phys. 106, 1965 (2008)]. The calculations were carried out by employing the relativistic coupled-cluster theory at the single, double, and involving important valence triple approximation. The accuracies of the calculated $B/Q$ results can be viewed on the basis of comparison between our calculated magnetic dipole hyperfine structure constants ($A$'s) with their corresponding measurements for many low-lying states. Both $A$ and $B$ results in a few more excited states are presented. Also, we find that the latest reported experimental hyperfine structure constant results for the $4P$ states in ${}^{39}$K are inconsistent with our calculations.

Correlation effects in Yb+and implications for parity violation

Calculation of the energies, magnetic dipole hyperfine structure constants, $E$1 transition amplitudes between the low-lying states, and nuclear spin-dependent parity-nonconserving amplitudes for the ${}^{2}{S}_{1/2}\ensuremath{-}{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2,5/2}$ transitions in ${}^{171}$Yb${}^{+}$ ion is performed using two different approaches. First, we carried out many-body perturbation theory calculation considering Yb${}^{+}$ as a monovalent system. Additional all-order calculations are carried out for selected properties. Second, we carried out configuration interaction calculation considering Yb as a 15-electron system and compared the results obtained by two methods. The accuracy of different methods is evaluated. We find that the monovalent description is inadequate for evaluation of some atomic properties due to significant mixing of the one-particle and the hole-two-particle configurations. Performing the calculation by such different approaches allowed us to establish the importance of various correlation effects for Yb${}^{+}$ atomic properties for future improvement of theoretical precision in this complicated system.

Measurements of hyperfine structure in 51V II

We have applied fast-ion-beam laser-fluorescence spectroscopy to measure the magnetic dipole hyperfine structure (hfs) constants of 24 even levels and 31 odd levels in 51V II. These are the first published data for hfs in this ion. These results will be very useful for the measurement of stellar photospheric abundances, studies of the history of nucleosynthesis and the testing of models of stellar interiors. The rather large hyperfine splittings in 51V II significantly affect the saturation and width of absorption lines, and this must be taken into account in order to derive accurate abundances and stellar rotation and micro- and macro-turbulence parameters, as well as to help determine if line blending is occurring.

Hyperfine structure study of atomic niobium with enhanced sensitivity of Fourier transform spectroscopy

In an experimental setup with a high-resolution Fourier transform (FT) spectrometer and a hollow-cathode discharge, bandpass interference filters are used to enhance the sensitivity. This extension leads to an improvement of the signal-to-noise ratio in the spectrum of atomic niobium by a factor of up to 10 compared to FT spectra measured previously without filters (see Kröger et al 2010 Astron. Astrophys. 516 A70). Several additional spectral lines with low intensity have been observed. Additionally, in some intense lines, blends become visible due to the better signal-to-noise ratio. The hyperfine structure of 51 lines recorded in the wavelength range from 415 to 670 nm is analysed or re-analysed and magnetic dipole hyperfine structure constants A of 8 levels of even parity and 43 levels of odd parity are determined. Improvement of sensitivity of FT spectroscopy in the visible wavelength range enabled the determination of new hyperfine structure constants A for two energy levels of even parity, which fill the last gaps for energetically low-lying levels below 14 000 cm−1. Additionally, ten new A constants for energetically higher lying levels of odd parity as well as several improved A values have been obtained.

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 ${\mathrm{Yb}}^{+}$.

Hyperfine structure measurements of neutral niobium with Fourier transform spectroscopy

Aims. We report on experimental studies of hyperfine structure splitting of neutral niobium.Methods. We used high-resolution Fourier transform spectroscopy to record a spectrum of niobium produced with a hollow cathode discharge lamp in the range of wavenumbers from 10 000 cm-1 to 30 000 cm-1 .Results. The magnetic dipole hyperfine structure constants A were determined for the 109 levels of odd parity by analyzing the profiles of 224 spectral lines. The A values of 57 of these level are reported for the first time.

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.

Hyperfine structure measurements of the even electron levels in scandium atom

Magnetic dipole hyperfine structure constants A for 19 even electron levels have been determined with the use of the method of laser-induced fluorescence in a hollow cathode discharge. In the case of 17 levels, the A constants have been obtained for the first time; in two cases the earlier literature values have been confirmed.

Relativistic calculations of the lifetimes and hyperfine structure constants in 67Zn+

This work presents accurate ab initio determination of the magnetic dipole (M1) and electric quadrupole (E2) hyperfine structure constants for the ground and a few low-lying excited states in 67Zn+, which is one of the interesting systems in fundamental physics. The coupled-cluster (CC) theory within the relativistic framework has been used here in these calculations. Long-standing demands for a relativistic and highly correlated calculation like CC can be able to resolve the disagreements among the lifetime estimations reported previously for a few low-lying states of Zn+. The roles of different electron correlation effects in the determination of these quantities are discussed and their contributions are presented.

Hyperfine structure investigation of Sc I, part II: theoretical studies of the odd configurations

Based on the experimental hyperfine structure data given in our previous study, the multi-configuration method has been used to calculate the fine structure of the odd parity configurations 3d4s4p, 4s2 4p and 3d2 4p of neutral Scandium taking into account configuration interaction effects. Magnetic dipole hyperfine structure constants are analysed in the effective-operator formalism for the isotope 45Sc. Relativistic one-electron parameters of the magnetic dipole hyperfine structure anlkskl(kskl= 01, 10, 12) were fitted to the experimental data by a least-squares fit procedure. Theoretical predictions for the magnetic dipole hyperfine structure constants A for all levels of the three configurations are given.

Many-body effects in hyperfine interactions in 205Pb+

Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of 205Pb+. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier.

Fine and hyperfine structure in the atomic spectrum of niobium

A parametric analysis of the fine and the magnetic dipole hyperfine structure for the three configurations of odd parity 4d35s5p, 4d45p and 4d25s25p was performed. Effective one-electron parameters were determined and theoretical predictions are given for the magnetic dipole hyperfine structure constants A for the levels of these three configurations. Additionally, 12 new energy levels could be found, four of odd and eight of even parity, by re-analysing data for experimental wavelengths of Nb.

Triple excitations in the relativistic coupled-cluster formalism and calculation of Na properties

A practical high-accuracy relativistic method of atomic structure calculations for univalent atoms is presented. The method is rooted in the coupled-cluster formalism and includes non-perturbative treatment of single and double excitations from the core and single, double and triple excitations involving valence electron. Triple excitations of core electrons are included in the fourth-order of many-body perturbation theory. In addition, contributions from the disconnected excitations are incorporated. Evaluation of matrix elements includes all-order dressing of lines and vertices of the diagrams. The resulting formalism for matrix elements is complete through the fourth order and sums certain chains of diagrams to all orders. With the developed method we compute removal energies, magnetic-dipole hyperfine-structure constants A and electric-dipole amplitudes. We find that the removal energies are reproduced within 0.01-0.03% and the hyperfine constants of the 3s_1/2 and 3p_1/2 states with a better than 0.1% accuracy. The computed dipole amplitudes for the principal 3s_1/2 - 3p_1/2;3/2 transitions are in an agreement with 0.05%-accurate experimental data.

Electron correlation effects in hyperfine interactions in 45Sc and 89Y

Relativistic coupled-cluster theory has been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants for the stable isotopes 45Sc and 89Y. The results are in good agreement with available experimental data. The role of electron correlation is found to be important. The trend exhibited by these effects in the systems under consideration with d-valence electrons is rather different from previously studied s and p single valence atomic systems. The contributions of certain higher order correlation effects are about 10–20%. Electric quadrupole hyperfine structure constants for 4d2D3/2 and 4d2D5/2 states are presented for the first time.

Application of relativistic coupled-cluster theory to heavy atomic systems with strongly interacting configurations: Hyperfine interactions inPb+207

This work presents a first time accurate calculation of the magnetic dipole hyperfine structure constants for the ground state and some low-lying excited states of Pb$^+$. By comparing different levels of approximation with experimental results, we demonstrate the importance of correlation effects which reach beyond lower order relativistic many body perturbation theory. Employing relativistic coupled-cluster theory we obtain a quantitative understanding of the core-polarization and correlation effects inherent in this system and observe completely different trends compared to $Ba^+$.