We have employed the relativistic coupled cluster theory to calculate the magnetic dipole and electric quadrupole hyperfine constants for the ground and low lying excited states of singly ionized magnesium. Comparison with experimental and the other theoretical results are done and predictions are also made for a few low lying excited states which could be of interest. We have made comparative studies of the important many body effects contributing to the hyperfine constants for the different states of the ion.
We report results of a theoretical investigation of hyperfine interactions in two homonuclear isotopologues of the hydrogen molecule: H$_{2}$ and D$_{2}$. We present a set of hyperfine coupling constants: spin-rotation, spin-spin dipole and, in the case of the D$_{2}$ molecule, electric quadrupole coupling constants for all bound states of the two isotopologues in their ground electronic $X^{1}Σ^{+}_{g}$ state. We provide a list of positions and intensities of 220 997 hyperfine components of 16 079 rovibrational quadrupole transitions of the O, Q and S branches. The positions and intensities o…
Spherically-symmetric ground states of alkali-metal atoms do not posses electric quadrupole moments. However, the hyperfine interaction between nuclear moments and atomic electrons distorts the spherical symmetry of electronic clouds and leads to non-vanishing atomic quadrupole moments. We evaluate these hyperfine-induced quadrupole moments using techniques of relativistic many-body theory and compile results for Li, Na, K, Rb, and Cs atoms. For heavy atoms we find that the hyperfine-induced quadrupole moments are strongly (two orders of magnitude) enhanced by correlation effects. We further a…
Reliability test for the experimental results of electric quadrupole hyperfine structure constants and new assessment of nuclear quadrupole moments in $^{135,137}$Ba
我们调查电四极超精细结构常数（$B$）的结果在$^{135}$ Ba $^+$和$^{137}$ Ba $^+$和比较它们的比率与报告的测量的比率之间的核四极矩（$Q$）值的这些同位素。我们进行了置信度测试报告的实验$B$值和计算的$B/Q$从目前的工作。在来自使用相同技术进行的不同实验的两种同位素中观察到实验$B$值的增加。本文的计算是用全阶相对论多体理论进行的，只考虑了耦合团簇中的单激发和双激发。在对结果进行详细分析后，我们获得的$^{135}$ Ba和$^{137}$ Ba的$Q$值分别为0.153（2）$b$和0.236（3）$b$，与目前引用的精确值相差约4%。
Accurate calculations of magnetic dipole and electric quadrupole hyperfine coupling constants of 6 P_{3/2} state of Cesium atom : A Relativistic Coupled Cluster approach
We evaluate the electric quadrupole moments of the ${^1}\!S_0$ and ${^3}\!P_0$ clock states of $^{27}$Al$^+$ and $^{115}$In$^+$. To capture all dominant contributions, our analysis extends through third order of perturbation theory and includes hyperfine coupling of the electrons to both the magnetic dipole and electric quadrupole moments of the nucleus. For $^{27}$Al$^+$, a fortuitous cancellation leads to a suppressed frequency shift. This should allow for continued improvement of the clock without special techniques to control or cancel the shift, such as the averaging schemes that are crit…
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 q…
Hyperfine-induced electric dipole contributions may significantly increase probabilities of otherwise very weak electric octupole and magnetic quadrupole atomic clock transitions (e.g. transitions between $s$ and $f$ electron orbitals). These transitions can be used for exceptionally accurate atomic clocks, quantum information processing and search for dark matter. They are very sensitive to new physics beyond the Standard Model, such as temporal variation of the fine structure constant, the Lorentz invariance and Einstein equivalence principle violation. We formulate conditions under which th…
We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest $^{1,3}\!P_J$, $^{3}\!S_1$, $^{3}\!P^e_J$, and $^{1,3}\!D_J$ excited states of the $^9$Be atom using explicitly correlated Gaussian functions and report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.
We have performed accurate calculations of the hyperfine structure of the $2\,^3\!P$ state in the $^9$Be atom with the help of highly optimized, explicitly correlated functions, accounting for the leading finite nuclear mass, radiative, nuclear structure and relativistic effects. By comparison with measurements, we have determined the $^9$Be nuclear quadrupole moment to be $Q_{\rm N} = 0.05350(14)$ barns, which is not only the most accurate result, but also disagrees with previous determinations.
The multi-configuration Dirac-Hartree-Fock method was employed to calculate the total and excitation energies, oscillator strengths and hyperfine structure constants for low-lying levels of Sm I. In the first-order perturbation approximation, we systematically analyzed correlation effects from each electrons and electron pairs. It was found that the core correlations are of importance for physical quantities concerned. Based on the analysis, the important configuration state wave functions were selected to constitute atomic state wave functions. By using this computational model, our excitatio…
Molecular hydrogen ions are of metrological relevance due to the possibility of precise theoretical evaluation of their spectrum and of external-field-induced shifts. In homonuclear molecular ions the electric dipole $E1$ transitions are strongly suppressed, and of primary laser spectroscopy interest is the electric quadrupole ($E2$) transition spectrum. In continuation of previous work on the H$_2^+$ ion, we report here the results of the calculations of the hyperfine structure of the laser-induced electric quadrupole transitions between a large set of ro-vibrational states of D$_2^+$; the in…
Large scale ab initio calculations of the electric contribution (i.e. the electric field gradient) to the electric quadrupole hyperfine interaction constants $B$ for the $5p~^2P_{3/2}$ state in $^{109}$Cd$^+$ ion and the $5s5p~^3P_{1,2}$ states in neutral $^{109}$Cd atom were performed. To probe the sensitivity of $B$ to different electron correlation effects, six sets of variational multi-configuration Dirac-Hartree-Fock and relativistic configuration interaction calculations employing different strategies were carried out. The calculated electric field gradients, together with experimental v…
Hyperfine-structure constants of odd Ra$^{+}$ due to the interactions of nuclear magnetic dipole, electric quadrupole, and magnetic octupole moments with the electrons are investigated in the framework of relativistic coupled-cluster method within single- and double-excitation approximation. The calculated energies and magnetic dipole hyperfine-structure constants $A$ exhibit a good agreement with available experimental values. Combining with the experimental electric quadrupole hyperfine-structure constant, we also extracted the electric quadrupole moments $Q$ of $^{209,211,221,223}$Ra. Our $…
The values of nuclear electric quadrupole moment are different by about 7% for 87Sr nucleus between the recommended value [N. J. Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); P. Pyykko, Mol. Phys. 116, 1328 (2018)] and earlier results [e.g. A. M. Matensson-Pendrill, J. Phys. B: At. Mol. Opt. Phys. 35, 917 (2002); K. Z. Yu et al., Phys. Rev. A 70, 012506 (2004)]. In this work, we reported a new value, Q(87Sr) = 328(4) mb, making use of our calculated electric field gradients produced by electrons at nucleus in combination with experimental values for hyperfine structures of the 5s5p 3P1,…
A method for precise calculation of the energy corrections due to second order electric quadrupole interactions, as well as mixed electric quadrupole-vacuum polarization in the framework of the dynamic hyperfine structure in heavy muonic atoms is presented. For this, a multipole expansion of the Uehling potential is performed. The approach is applicable for an arbitrary nuclear electric charge distribution. By performing these calculations for muonic Rhenium and Uranium using a deformed Fermi distribution, it is shown that both corrections contribute on a level presumably visible in upcoming e…
We consider hyperfine-mediated effects for clock transitions in $^{176}$Lu$^+$. Mixing of fine structure levels due to the hyperfine interaction bring about modifications to Landé $g$-factors and the quadrupole moment for a given state. Explicit expressions are derived for both $g$-factor and quadrupole corrections, for which leading order terms arise from the nuclear magnetic dipole coupling. High accuracy measurements of the $g$-factors for the $^1S_0$ and $^3D_1$ hyperfine levels are carried out, which provide an experimental determination of the leading order correction terms.
We report the value of the electric quadrupole moment of $^{209}$Bi extracted from the atomic data. For this, we performed electronic structure calculations for the ground $^4S^o_{3/2}$ and excited $^2P^o_{3/2}$ states of atomic Bi using the Dirac-Coulomb-Breit Hamiltonian and the Fock space coupled cluster method with single, double, and full triple amplitudes for the three-particle Fock space sector. The value of the quadrupole moment of $^{209}$Bi, $Q(^{209}$Bi$)=-418(6)$~mb, derived from the resulting electric field gradient values and available atomic hyperfine splittings is in excellent …
The present work determines the precise values of magic wavelengths corresponding to the clock transitions 5$^2S$-4$^2D$ of Y$^{2+}$ ion both at the levels of fine- and hyperfine-structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substan…
The hyperfine structures of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states of the $^7$Be$^{2+}$ and $^9$Be$^{2+}$ ions are investigated within the framework of the nonrelativistic quantum electrodynamics (NRQED). The uncertainties of present hyperfine splitting results of $^9$Be$^{2+}$ are in the order of several tens of ppm, where two orders of magnitude improvement over the previous theory and experiment values has been achieved. The contribution of nuclear electric quadrupole moment to hyperfine splitting of $^7$Be$^{2+}$ has been studied. A scheme for determining the properties of Be nuclei in t…
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 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 229Th^(3+)…
We show that by averaging over transitions to multiple hyperfine levels, quadrupole shifts and dominant Zeeman effects exactly cancel whenever the nuclear spin, I, is at least as large as the total electronic angular momentum, J. The average frequency thus defines a frequency reference which is inherently independent of external magnetic fields and electric field gradients. We use Lu+ to illustrate the method although the approach could be readily adapted to other atomic species. This approach practically eliminates the quadrupole and Zeeman shift considerations for many clock candidates.
We investigate interactions between the proton spin, the deuteron spin, and the orbital angular momentum in the electronic ground state of the HD molecule. These interactions lead to hyperfine splittings of molecular energy levels. Our numerical results for the first rotational level agree well with the currently most accurate measurement performed by Ramsey {\em et al.} in the 1950s. Knowledge of the hyperfine structure of other levels is necessary for the accurate determination of rovibrational transition energies in spectroscopic measurements. We present theoretical predictions and share th…
The thorium nucleus with mass number $A=229$ has attracted much interest because its extremely low lying first excited isomeric state at about $8$eV opens the possibility for the development of a nuclear clock. However, neither the exact energy of this nuclear isomer nor properties, such as nuclear magnetic dipole and electric quadrupole moment are known to a high precision so far. The latter can be determined by investigating the hyperfine structure of thorium atoms or ions. Due to its electronic structure and the long lifetime of the nuclear isomeric state, Th$^{2+}$ is especially suitable f…
Energy levels, magnetic dipole, and electric quadrupole hyperfine structure of the superheavy element rutherfordium (Rf, $Z$=104) and its first three ions are calculated using a combination of the configuration interaction, coupled-cluster single-doubles, and many-body perturbation theory techniques. The results are to be used in future interpretations of the measurements in terms of nuclear magnetic dipole and electric quadrupole momenta. To have a guide on the accuracy of the study, we perform similar calculations for hafnium (Hf, $Z$=72) and its ions. Hf is a lighter analog of Rf with a sim…
We demonstrate the importance of electron correlation effects in the hyperfine structure constants of many low-lying states in $^{210}$Fr and $^{212}$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 …
A recently developed version of the configuration interaction (CI) method for open shells with a large number of valence electrons has been used to study two heavy atoms, californium (Cf, Z= 98) and einsteinium (Es, Z= 99). Motivated by experimental work to measure the hyperfine structure (HFS) for these atoms, we perform the calculations of the magnetic dipole HFS constants $A$ and electric quadrupole HFS constant $B$ for the sake of interpretation of the measurements in terms of nuclear magnetic moment $μ$ and electric quadrupole moment $Q$. For verification of our computations, we have also…
Narrow linewidth signals of Electromagnetically Induced Transparency (EIT) in the metastable 83Kr have been observed for the first time. Various hyperfine transitions in 4p55s[3/2]2 to 4p55p[5/2]3 manifolds of 83Kr have been identified through the experimentally observed EIT signals. Some unresolved or poorly resolved hyperfine transitions in saturated absorption spectroscopy (SAS) are clearly resolved in the present work. Using the spectral separation of these EIT identified hyperfine transitions, the magnetic hyperfine constant (A) and the electric quadrupole hyperfine constant (B) are deter…
In this paper we present tabulated data for magnetic-dipole-to-electric-quadrupole cross-susceptibilities ($χ_{\textrm{M}1 \to \textrm{E}2}$) for Dirac one-electron atoms with a pointlike, spinless and motionless nucleus of charge $Ze$. Numerical values of this susceptibility for the hydrogen atom ($Z=1$) and for hydrogenic ions with $2 \leqslant Z \leqslant 137$ are computed from the general analytical formula, recently derived by us [P. Stefa{ń}ska, Phys. Rev. A 93 (2016) 022504], valid for an arbitrary discrete energy eigenstate. In this work we provide 30 tables with the values of $χ_{\tex…
Large-scale $\textit{ab initio}$ calculations of the electric field gradient, which constitutes the electronic contribution to the electric quadrupole hyperfine constant $B$, were performed for the $5s^25p6s$ $^{1,3}\!P^{\rm o}_1$ excited states of tin, using three independent computational strategies of the variational multiconfiguration Dirac-Hartree-Fock method and a fourth approach based on the configuration interaction Dirac-Fock-Sturm theory. For the $5s^25p6s$ $^{1}\!P^{\rm o}_1$ state, the final value of $B/Q =703(50)$ MHz/b differs by $0.4\%$ from the one recently used by Yordanov ${\…
Advances in laser spectroscopy of superheavy ($Z>100$) elements enabled determination of the nuclear moments of the heaviest nuclei, which requires high-precision atomic calculations of the relevant hyperfine structure (HFS) constants. Here, we calculated the HFS constants and energy levels for a number of nobelium (Z=102) states using the hybrid approach, combining linearized coupled-cluster and configuration interaction methods. We also carried out an extensive study of the No energies using 16-electron configuration interaction method to determine the position of the (5f^{13}7s^2 6d) and (5…
