Magnetic Dipole Hyperfine Constants Research Articles

Large-scale multiconfiguration Dirac-Hartree-Fock calculations of atomic data, Landé gj -factors and hyperfine constants of the neutral Rn-211 isotope

We computed the atomic data of ns[K]J ( n = 7, 8, 9), np[K]J ( n = 7, 8, 9), nd[K]J ( n = 6, 7, 8, 9), and nf[K]J ( n = 5, 6, 7, 8) and 5g[K]J autoionized Rydberg spectra of the neutral radon-211 isotope. The computations are carried out by using the Multiconfiguration Dirac-Hartree-Fock method (MCDHF) together with the relativistic configuration (RCI) approach. The convergence of the obtained results is monitored by incorporating relativistic electron-electron correlation, the Breit-interaction effect, self-energy, and vacuum-polarization corrections. As a result, we acquired the energy levels, transition rates, oscillator strengths, Landé gJ -factors and magnetic dipole hyperfine constants. The transition parameters between the levels belonging to different series are computed for all allowed electric dipole transition selection rules. The present results are in very good agreement with other experimental and theoretical data available in the literature database. The present data could be useful in predicting spectral lines of radon via astrophysics and stellar spectroscopy.

Variation of the Quadrupole Hyperfine Structure and Nuclear Radius due to an Interaction with Scalar and Axion Dark Matter.

Atomic spectroscopy is used to search for the space-time variation of fundamental constants which may be due to an interaction with scalar and pseudoscalar (axion) dark matter. In this Letter, we study the effects that are produced by the variation of the nuclear radius and electric quadrupole moment. The sensitivity of the electric quadrupole hyperfine structure to both the variation of the quark mass and the effects of dark matter exceeds that of the magnetic hyperfine structure by 1-2 orders of magnitude. Therefore, the measurement of the variation of the ratio of the electric quadrupole and magnetic dipole hyperfine constants is proposed. The sensitivity of the optical clock transitions in the Yb^{+} ion to the variation of the nuclear radius allows us to extract, from experimental data, limits on the variation of the hadron and quark masses, the QCD parameter θ and the interaction with axion dark matter.

Tin resonance-ionization schemes for atomic- and nuclear-structure studies

This paper presents high-precision spectroscopic measurements of atomic tin using five different resonance-ionization schemes performed with the collinear resonance-ionization spectroscopy technique. Isotope shifts were measured for the stable tin isotopes from the $5{s}^{2}5{p}^{2}\phantom{\rule{0.28em}{0ex}}^{3}{P}_{0,1,2}$ and ${}^{1}{S}_{0}$ to the $5{s}^{2}5p6s\phantom{\rule{0.28em}{0ex}}^{1}{P}_{1},^{3}{P}_{1,2}$ and $5{s}^{2}5p7s{\phantom{\rule{0.28em}{0ex}}}^{1}{P}_{1}$ atomic levels. The magnetic dipole hyperfine constants ${A}_{\mathrm{hf}}$ have been extracted for six atomic levels with electron angular momentum $Jg0$ from the hyperfine structures of nuclear spin $I=1/2$ tin isotopes, $^{115,117,119}\mathrm{Sn}$. State-of-the-art atomic calculations using a relativistic Fock-space coupled-cluster method and the configuration interaction approach combined with many-body perturbation theory allow accurate and reliable calculations of both field- and mass-shift factors for the studied transitions, in addition to the hyperfine magnetic fields and electric-field gradients of the atomic levels. The excellent agreement with the experimental results highlights the accuracy of modern atomic theory and establishes an important foundation for precision measurements of nuclear moments and charge radii of the most exotic isotopes of tin.

Theoretical analysis of the relativistic hyperfine interaction in 131Xe I

The relativistic hyperfine constants of the heavy inert gas element xenon-131 isotope have been calculated. The calculations, executed through the Multiconfiguration Dirac-Hartree-Fock method, yield the hyperfine constants of 128 levels belonging to the ns[K]J (n = 6, 7, 8, 9), nf [K]J (n = 4, 5, 6), nd[K]J (n = 5, 6, 7, 8), np[K]J (n = 6, 7, 8) and 5g[K]J intermediate Rydberg series. In order to draw further insights into the precision of our calculations and the accuracy of the obtained data, the resulting magnetic dipole and electric quadrupole hyperfine constants are analysed by comparing them with other experimental and theoretical results available in the atomic spectra database. Indeed, a satisfactory agreement is observed between our results and the other experimental and theoretical ones. Moreover, the absence of the hyperfine anomaly enables us to highlight the plausibility of our theoretical results through the calculation of the ratio A129A131 for a given state. The obtained values are found to be compatible with the ratio of nuclear moments of 129Xe and 131Xe isotopes. The consistency of these two different analyses confirms the accuracy of our data, on the one hand and classifies them as a reference in identifying the experimental spectrum in xenon, on the other hand. Based on this accuracy, the calculated values of the hyperfine constants for the levels under consideration, accompanied by the experimental values of the nuclear magnetic dipole and electric quadrupole moments, facilitated the calculation of the mean value of the magnetic as well as the electric field gradients produced by the electron at the tiny nucleus.

Atomic data of 5g[K]J, 6f[K]J, nd[k]j (n = 7, 8), 8p[K]J and 9s[K]J autoionizing Rydberg series of 129Xe I

The energy levels, oscillator strengths, transition rates, Landé gJ-factors and magnetic dipole hyperfine constant for the 5g[K]J, 6f[K]J, nd[K]J (n = 7, 8), 8p[K]J and 9s[K]J autoionizing Rydberg series of 129Xe have been computed. The computations, were carried out relative to the ground state in the multiconfiguration Dirac-Hartree-Fock framework. Owing to restrictions imposed by electric dipole selection rules, the transitions from the ground state to the levels 8p, 5g and 6f levels are forbidden, therefore we computed all the 5p5(2P)6p-5p5(2P)8d, 5p5(2P)7p-5p5(2P)nd (n = 7, 8), 5p5(2P)5d-5p5(2P)8p, 5p5(2P)ns-5p5(2P)8p (n = 6, 7, 8) , 5p5(2P)6d-5p5(2P)8p, 5p5(2P)nd-5p5(2P)8p (n = 7, 8), 5p5(2P)nf-5p5(2P)7d (n = 4, 5) and 5p5(2P)nf-5p5(2P)5g (n = 4, 5) oscillator strengths and transition rates. In order to check the accuracy of the obtained data, the current theoretical results are compared with other earlier experimental and theoretical data available in the literature. In general, a high level of agreement has been observed for most of the levels. The present data is a continuation of our previous theoretical data calculated for 129Xe I (W. Salah, O. Hassouneh, Results in Physics, 12, 153 (2019)).

The relativistic computations of spectral lines of 129Xe I

Abstract In this paper, we present our achievement on the relativistic computations of the spectral lines for the levels belonging to the 6s[k]J, 4f[k]J, 5d[k]J, 6p[k]J, 7s[k]J, 5f[k]J, 6d[k]J, 7p[k]J and 8s[k]J intermediate Rydberg series in the heavy xenon-129 isotope. These spectral lines are identified by the energy levels, the transition rates, the oscillator strengths, the Lande gj-factors and the magnetic dipole hyperfine constant. Inasmuch as the transitions from the ground state to the 4f and 5f levels in addition to the 6p and 7p levels are forbidden by electric dipole selection rules, we computed all the 5p55d–5p5nf (4 ≤ n ≤ 5), 5p55d–5p5np (6 ≤ n ≤ 7), 5p56s–5p5np (6 ≤ n ≤ 7), 5p57s–5p56p, 5p56d–5p5nf (4 ≤ n ≤ 5), 5p56d–5p5np (6 ≤ n ≤ 7), 5p57s–5p57p and 5p58s–5p5np (6 ≤ n ≤ 7) transition arrays. The present accurate values of spectral lines are obtained by using the well-established multiconfiguration Dirac-Hartree-Fock (MCDHF) method in conjunction with the relativistic configuration interaction (RCI) calculations. The RCI calculations encompass further electron correlation effects. These effects include static electron-valence and core-valence correlation and core polarizations effects, the Breit and quantum electrodynamics (QED) corrections in addition to the effect of nuclear charge distribution. To provide a context for information in the accuracy associated with these values, a detailed comparison of our data with other experimental and theoretical data available in the database is made. On the whole, a good agreement has generally been observed for most of the spectral lines. These newcomers to the area of database with insights into nuclear fusion research, as they may provide diagnostic information on magnetically confined plasmas, they could be a reference point for the identification and de-blending of new spectral lines provided by astrophysics observations and space research.

Extensive and accurate relativistic calculations of atomic data on the 83Kr I spectrum

We provide an extensive, accurate and complete new spectroscopic data set for many levels belonging to the intermediate perturbing Rydberg series ns[K]J (5 ≤ n ≤ 8), nd[K]J (4 ≤ n ≤ 7) and the autoionizing Rydberg series np[K]J (5 ≤ n ≤ 7) and nf[K]J (4 ≤ n ≤ 5) relative to the ground state 4p6 1S0 for neutral krypton-83 isotope. The data set is composed of the energy levels, the oscillator strengths the radiative transition rates the Landé g-factors, the magnetic dipole and electric quadrupole hyperfine constants. The values of these spectroscopic parameters are calculated in the multiconfiguration Dirac-Hartree–Fock (MCDHF) framework. The calculations are carried out in the active space where the electron correlation effects, contributions from relativistic configuration interaction (RCI), the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization, specific mass shift and self-energy corrections are included. In addition, we provide the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 4p5(2P)4d–4p5(2P)5p, 4p5(2P)5s–4p5(2P)5p, 4p5(2P)6s–4p5(2P)5p, 4p5(2P)4d–4p5(2P)44f, 4p5(2P)5d–4p5(2P)4f, 4p5(2P)5d–4p5(2P)6p, 4p5(2P)7s–4p5(2P)6p, 4p5(2P)4d–4p5(2P)5f, 4p5(2P)5d–4p5(2P)5f, 4p5(2P)6d–4p5(2P)5f, 4p5(2P)7p–4p5(2P)6d and 4p5(2P)8s–4p5(2P)7p transition arrays. Extensive comparisons with other experimental and theoretical data from the reference databases are carried out in order to judge the reliability of our data. These comparisons indicate that our results are accurate. The present spectroscopic data may be useful for line identification in observed spectra as well as modelling and diagnostics of astrophysical and fusion plasmas.

Revised energy levels of singly ionized lanthanum

Based on the experimental wavenumbers of 344 spectral lines from calibrated Fourier transform (FT) spectra as well as wavenumbers of 81 lines from the wavelength tables from literature, the energy of 115 fine structure levels of singly ionized lanthanum has been revised by weighted global fits. The classifications of the lines are provided by numerous previous investigations of lanthanum by different spectroscopic methods and authors. For the high accurate determination of the center of gravity wavenumbers from the experimental spectrum, the hyperfine constants of the involved levels have been taken into account, if possible. For the 94 levels with known hyperfine constants the accuracy of energy values is better than 0.01 cm−1. For 34 levels the magnetic dipole hyperfine constants A have been determined from FT spectra as part of this work. For four of these 34 levels even electric quadrupole hyperfine constants B could be estimated. For levels, which have experimentally unknown hyperfine constants and which are connected only by lines not found in the FT spectra but taken from literature, the uncertainties of energy values are about a factor of 10 higher. A list of all revised level energies together with a compilation of hyperfine structure data is given as well as a list of all lines used.

Magnetic dipole and electric quadrupole hyperfine constants for V II 3d4, 3d3 4s and 3d2 4s2J = 1–5 states

Relativistic configuration interaction (RCI) calculations have been done for hyperfine constants and Lande g-values for 69 even parity V II states. Our results are in good agreement with the few recent experimental magnetic dipole results. We suggest that several Lande g-values need to be re-measured. Our electric quadrupole constants seem to be the first ones available. Analysis and methodology improvements include the introduction of an approximate sum rule for hyperfine constants, and a way of producing a more diagonal reference basis function set. The importance of mixing of 3dn−1 4s basis members with near degenerate 3dn or 3dn−2 4s2 is emphasized.

Hyperfine structure of laser-cooling transitions in fermionic erbium-167

We have measured and analyzed the hyperfine structure of two lines, one at 583nm and one at 401nm, of the only stable fermionic isotope of atomic erbium as well as determined its isotope shift relative to the four most-abundant bosonic isotopes. Our work focuses on the J->J+1 laser cooling transitions from the [Xe] 4f12 6s2 (3H6) ground state to two levels of the excited [Xe] 4f12 6s6p configuration, which are of major interest for experiments on quantum degenerate dipolar Fermi gases. From a fit to the observed spectra of the strong optical transition at 401nm we find that the magnetic dipole and electric quadrupole hyperfine constants for the excited state are Ae/h=-100.1(3)MHz and Be/h=-3079(30)MHz, respectively. The hyperfine spectrum of the narrow transition at 583nm, was previously observed and accurate Ae and Be coefficients are available. A simulated spectrum based on these coefficients agrees well with our measurements. We have also determined the hyperfine constants using relativistic configuration-interaction ab initio calculations. The agreement between the ab initio and fitted data for the ground state is better than 0.1%, while for the two excited states the agreement is 1% and 11% for the Ae and Be constants, respectively.

Spectroscopy on a single trapped ^137Ba^+ ion for nuclear magnetic octupole moment determination

We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, 137 Ba+ . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magnetic octupole constant (C) with an accuracy below 0.1 Hz. This gives a subsequent determination of the nuclear magnetic octupole moment, {\Omega}, with an uncertainty of 1% limited almost completely by the accuracy of theoretical calculations. This constitutes the first observation of the octupole moment in 137 Ba+ and the most accurately determined octupole moment to date.

Coupled-cluster calculations of properties of the boron atom as a monovalent system

We present relativistic coupled-cluster (CC) calculations of energies, magnetic-dipole hyperfine constants, and electric-dipole transition amplitudes for low-lying states of atomic boron. The trivalent boron atom is computationally treated as a monovalent system. We explore performance of the CC method at various approximations. Our most complete treatment involves singles, doubles and the leading valence triples. The calculations are done using several approximations in the coupled-cluster (CC) method. The results are within 0.2-0.4% of the energy benchmarks. The hyperfine constants are reproduced with 1-2% accuracy.

Hyperfine structure of the 3d34s4p 6G multiplet of atomic vanadium

The spectrum of atomic vanadium was recorded using high-resolution Fourier transform spectroscopy with optical bandpass filters in the wavelength range from 360 to 500 nm. Vanadium atoms are produced and excited in a hollow-cathode discharge. The main focus lies on the determination of the magnetic dipole hyperfine constants A of the lowest multiplet of odd parity, the 6G of the configuration 3d34s4p, the hyperfine structure (HFS) of which was unknown to date. The HFS of the lines, connecting this multiplet with the multiplets 3d34s5s 6F, 3d34s4d 6H and 3d34s4d 6G, was observed and analysed. New results are presented for all six levels belonging to 3d34s4p 6G as well as for seven high-lying levels belonging to 3d34s4d 6H and 3d34s4d 6G. The experimental results for the lowest multiplet of odd parity are compared with calculated magnetic dipole hyperfine constants which were estimated using the effective-operator formalism in the pure LS coupling case.

Wigner Crystals ofTh229for Optical Excitation of the Nuclear Isomer

We have produced laser-cooled Wigner crystals of 229Th3+ in a linear Paul trap. The magnetic dipole (A) and electric quadrupole (B) hyperfine constants for four low-lying electronic levels and the relative isotope shifts with respect to 232Th3+ for three low-lying optical transitions are measured. Using the hyperfine B constants in conjunction with prior atomic structure calculations, a new value of the spectroscopic nuclear electric quadrupole moment Q=3.11(16) eb is deduced. These results are a step towards optical excitation of the low-lying isomer level in the 229Th nucleus.

Atomic properties calculated by relativistic coupled-cluster theory without truncation: Hyperfine constants ofMg+,Ca+,Sr+, andBa+

We demonstrate an iterative scheme for coupled-cluster properties calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline Earth ions are calculated with relativistic coupled-cluster and role of electron correlation examined. Then, a detailed analysis of the higher order terms is carried out. Based on the results, we arrive at an optimal form of the dressed operator. Which we recommend for properties calculations with relativistic coupled-cluster theory.

Publisher's Note: Nuclear quadrupole moment ofC43aand hyperfine-structure studies of its singly charged ion [Phys. Rev. A80, 012515 (2009)

By combining our theoretical calculation and recently measured electric quadrupole hyperfine structure constant of the $3d ^2D_{5/2}$ state in the singly ionized $^{43}$Ca, we determine its nuclear quadrupole moment to one percent accuracy. The obtained result, $-0.0444(6)b$, is about ten percent improvement over the considered standard value. We have employed the relativistic coupled-cluster theory at single and double excitations level to calculate the electronic wave functions. The accuracy of these wave functions are estimated by comparing our calculated magnetic dipole hyperfine constants with their corresponding available experimental results of many low-lying states. We also present hyperfine structure constants for other higher excited states where experimental results are not reported. Role of the Breit interaction has been investigated in these properties.

Nuclear quadrupole moment ofC43aand hyperfine-structure studies of its singly charged ion

By combining our theoretical calculation and the recently measured electric quadrupole hyperfine-structure constant of the $3d\text{ }{^{2}D}_{5/2}$ state in the singly ionized $^{43}\text{C}\text{a}$, we determine its nuclear quadrupole moment to 1% accuracy. The obtained result, $\ensuremath{-}0.0444(6)b$, is about 10% more accurate over its current accepted value. We have employed the relativistic coupled-cluster theory at the single and double excitations level to calculate the atomic wave functions. The accuracy of these wave functions is estimated by comparing our calculated magnetic dipole hyperfine constants with their corresponding available experimental results of many low-lying states. We also present hyperfine-structure constants for other higher excited states where experimental results are not reported. The role of the Breit interaction has been investigated in these properties.

Comment on the magnetic dipole hyperfine interaction in the gold atom ground state

The multiconfiguration Dirac–Hartree–Fock (MCDHF) model has been employed to calculate the magnetic dipole hyperfine constant A of the 5d106s 2S1/2 ground state of atomic gold. Electron correlation effects contribute more than 20% to the total value of A. We investigated the effects of single, double, and a subset of triple substitutions. The calculations reveal strong cancellations between one-, two- and three-particle correlation effects. It is demonstrated that in the case of the ground state of atomic gold the three-particle effects are comparable in size to the one- and two-particle ones.

Nuclear Magnetic Moment ofFr210: A Combined Theoretical and Experimental Approach

We measure the hyperfine splitting of the 9S_{1/2} level of 210Fr, and find a magnetic dipole hyperfine constant A=622.25(36) MHz. The theoretical value, obtained using the relativistic all-order method from the electronic wave function at the nucleus, allows us to extract a nuclear magnetic moment of 4.38(5)micro_{N} for this isotope, which represents a factor of 2 improvement in precision over previous measurements. The same method can be applied to other rare isotopes and elements.

Relativistic unitary coupled cluster theory and applications

We present the formulation and application of relativistic unitary coupled cluster theory to atomic properties. The remarkable features of this theory are highlighted, and it is used to calculate the lifetimes of 5d2D3/2 and 6p2P3/2 states of Ba+ and Pb+ respectively. The magnetic dipole hyperfine constants for the 6s2S1/2 state of Ba+ and the 6p2P3/2 state of Pb+ have also been calculated. The results clearly suggest that it is very well suited for accurate ab initio calculations of properties of heavy atomic systems. The present calculation of lifetime for Ba+ gives an improvement over the previously calculated values using ordinary coupled-cluster theory, although we have observed that the decay of the excited state via the magnetic dipole channel is even more important.