Accurate predictions of hyperfine structure (HFS) constants are important in many areas of chemistry and physics, from the determination of nuclear electric and magnetic moments to benchmarking of new theoretical methods. We present a detailed investigation of the performance of the relativistic coupled cluster method for calculating HFS constants withing the finite-field scheme. The two selected test systems are $^{133}$Cs and $^{137}$BaF. Special attention has been paid to construct a theoretical uncertainty estimate based on investigations on basis set, electron correlation and relativistic effects. The largest contribution to the uncertainty estimate comes from higher order correlation contributions. Our conservative uncertainty estimate for the calculated HFS constants is $\sim$ 5.5\%, while the actual deviation of our results from experimental values was $<1$\% in all cases.
In previous work devoted to {\it ab initio} calculations of hyperfine structure constants in nitrogen and fluorine atoms, we observed sizeable relativistic effects, a priori unexpected for such light systems, that can even largely dominate over electron correlation. We observed that the atomic wave functions calculated in the Breit-Pauli approximation describe adequately the relevant atomic levels and hyperfine structures, even in cases for which a small relativistic $LS$-term mixing becomes crucial. In the present work we identify new levels belonging to the spectroscopic terms $2p^4(^3\!P) 3…
Hyperfine structures and Landé $g_J$-factors for $n=2$ states in beryllium-, boron-, carbon-, and nitrogen-like ions from relativistic configuration interaction calculations
Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements and static polarizabilities for alkali-metal atoms
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 $…
Relativistic coupled cluster calculations on hyperfine structures and electromagnetic transition amplitudes of In III
用高关联相对论耦合团簇理论研究了$^{113,115,117}$ In III的基态和低激发态的超精细常数和反常。$^{115}$ In III的基态超精细分裂估计为106.8 GHz。由于修改核偶极矩，上述频率的近1.9 GHz的位移已被计算。该分裂结果显示了其作为$10^{-11}$秒的通信频带和频率标准的适用性。超精细常数的关联研究表明，该离子核区及其附近的波函数具有明显的多体效应特征。据我们所知，首次在文献中估计了天体物理上重要的禁戒跃迁振幅。计算的振子强度的几个允许的过渡与最近的实验和理论结果进行比较。
Level-crossing spectroscopy of the 7, 9, and 10D_5/2 states of 133Cs and validation of relativistic many-body calculations of the polarizabilities and hyperfine constants
We have developed an all-particle Fock-space relativistic coupled-cluster method to calculate the properties of two-valence atoms and ions. Using the method we compute the properties associated with hyperfine induced $^1S_0 - ^3P^o_0$ clock transition in Al$^+$. Our result of the $^3P^o_0$ metastable state life time, $20.20 \pm 0.91$ s, is in excellent agreement with the experimental value, $20.60 \pm 1.4$ s [Phys. Rev. Lett. {\bf 98}, 220801 (2007)]. Our studies show that the contributions from the triple excitations, and the corrections from the Breit interaction and QED effects are essentia…
Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the $2p^{5}~^{2}P^{o}$, $2p^4(^{3}P)3s~^{4}P$, $2p^4(^{3}P)3s~^{2}P$ and $2p^4(^{3}P)3p~^{4}S^o$ states of $^{19}$F~I to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference (SD-MR) expansions. The largest components of the single reference MCHF wave functions are selected to …
Neutral uranium (U I) is a very difficult atom for theoretical calculations due to a large number of valence electrons, six, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can treat efficiently valence-core correlations and relativistic effects, but because the formalism was developed for Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for +6 charge of such a potential. Much more efficient is…
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
Properties from relativistic coupled-cluster without truncation: hyperfine constants of $^{25}{\rm Mg}^+$, $^{43}{\rm Ca}^+ $, $^{87}{\rm Sr}^+ $ and $^{137}{\rm Ba}^+$
$^{229}$Th is a promising candidate for developing a nuclear optical clock and searching the new physics beyond the standard model. Accurate knowledge of the nuclear properties of $^{229}$Th is very important. In this work, we calculate hyperfine-structure constants for the first four states of $^{229}$Th$^{3+}$ using the relativistic coupled-cluster method based on the Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, together with all linear and non-linear terms of single and double excitations a…
Application of Relativistic Coupled-cluster Theory to Heavy Atomic Systems with Strongly Interacting Configurations: Hyperfine Interactions in $^{207}Pb^+$
NRQED approach to the fine and hyperfine structure corrections of order m$α$ 6 and m$α$ 6 (m/M)-Application to the hydrogen atom The NRQED approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m$α$ 6 and m$α$ 6 (m/M). Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, and may be used for studying more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used …
Calculations of the magnetic hyperfine structure rely on the input of nuclear properties -- nuclear magnetic moments and nuclear magnetization distributions -- as well as quantum electrodynamic (QED) radiative corrections for high-accuracy evaluation in heavy atoms. The uncertainties associated with assumed values of these properties limit the accuracy of hyperfine calculations. For example, for the heavy alkali-metal atoms Cs and Fr, these uncertainties may amount collectively to almost 1\% or 2\%, respectively. In this paper we propose a method for removing the dependence of hyperfine struct…
Calculation of hyperfine structure constants of small molecules using Z-vector method in the relativistic coupled-cluster framework
采用相对论耦合集团框架下的Z矢量方法，计算了几种碱土金属小分子化合物（BeH，MgH，CaH）和氟化物（MgF，CaF）的磁超精细结构常数的平行分量和垂直分量.我们将我们的Z矢量结果与Phys. Rev. A 91 022512（2015）中报道的扩展耦合簇（ECC）方法计算的值进行了比较。所有这些结果与现有的实验值进行了比较。Z矢量的结果被发现是更好地符合实验值比ECC值。
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,…
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 have performed high-precision calculations of the hyperfine structure for n 2S_1/2 and n 2P_1/2 states of the alkali-metal atoms Rb, Cs, and Fr across principal quantum number n, and studied the trend in the size of the correlations. Our calculations were performed in the all-orders correlation potential method. We demonstrate that the relative correlation corrections fall off quickly with n and tend towards constant and non-zero values for highly-excited states. This trend is supported by experiment, and we utilize the smooth dependence on n to make high-accuracy predictions of the hyperfi…
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…
We are reinvestigating the hyperfine structure of sodium using a fully relativistic multiconfiguration approach. In the fully relativistic approach, the computational strategy somewhat differs from the original nonrelativistic counterpart used in Jönsson et al. (Phys. Rev. A 53 (1996) 4021). Numerical instabilities force us to use a layer-by-layer approach that has some broad unexpected effects. Core correlation is found to be significant and therefore requires to be described in an adequate orbital basis. The natural-orbital basis provides an interesting alternative to the orbital basis from …
Relativistic Calculation of Energies, Transition Parameters Hyperfine Structure, Landé g$_J$ and Isotope shifts factors for Ar$^{7+}$, Kr$^{25+}$ and Xe$^{43+}$ ions
The four-component relativistic Fock space coupled cluster method is used to describe the magnetic hyperfine interaction in low-lying electronic states of the KCs molecule. Both diagonal and off-diagonal matrix elements as functions of the internuclear separation $R$ are calculated within the finite-field scheme. The resulting matrix elements exhibit very weak dependence on $R$ for the separations exceeding 8 Å, whereas in the vicinity of the ground-state equilibrium the deviation of molecular HFS matrix elements from the atomic values reaches 15\%. The dependence of the computed HFS couplings…
Analysis of hyperfine structure constants of singly ionised cobalt (Co II) were performed on cobalt spectra measured by Fourier transform spectrometers in the region $3000-63000$ cm$^{-1}$ ($3333-159$ nm). Fits to over $700$ spectral lines led to measurements of $292$ magnetic dipole hyperfine interaction $A$ constants, with values between $-32.5$ mK and $59.5$ mK ($1$ mK $=0.001$ cm$^{-1}$). Uncertainties of $255$ A constants were between $\pm0.4$ mK and $\pm3.0$ mK, the remaining $37$ ranged up to $\pm7$ mK. The electric quadrupole hyperfine interaction $B$ constant could be estimated for on…
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…
A complete effective Hamiltonian for relativistic corrections at orders $mα^6$ and $mα^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calcu…
The static and dynamic electric-dipole polarizabilities and tune-out wavelengths for the ground state of Cs atoms are calculated by using a semiempirical relativistic configuration interaction plus core polarization approach. By considering the hyperfine splittings, the static and dynamic polarizabilities, hyperfine Stark shifts, and tune-out wavelengths of the hyperfine components of the ground level of $^{133}$Cs atoms are determined. It is found that the hyperfine shifts of the first primary tune-out wavelengths are about $-$0.0135 nm and 0.0106 nm, which are very close to the hyperfine int…
Theoretical study on the hyperfine interaction constants and the isotope shift factors for the $3s^2~^1 S_{ 0} ~-~ 3s3p~^{3,1}P^o_1$ transitions in Al$^+$
用多组态Dirac-Hartree-Fock方法计算了Al $^+$离子3s 3 p $^{3,1}P^o_1$态的磁偶极和电四极超精细相互作用常数，以及从这两个态到基态3s $^2~^1S_0$跃迁的同位素位移因子，包括质量和场位移因子.基于活性空间方法，详细研究了电子关联和Breit相互作用对这些物理量的影响。计算结果表明，CC和高阶关联对于评价原子参数的不确定度是相当重要的。超精细相互作用常数的不确定度小于1.5%.虽然同位素位移因子对电子关联高度敏感，但通过探索电子关联的影响，获得了合理的不确定性。此外，我们还发现Al $^{+}$的质量移动因子的相对论核反冲修正很小，对电子关联不敏感。这些原子参数对提取Al同位素的核电四极矩和均方电荷半径具有重要的参考价值。
We present an investigation of the performance of the relativistic multi-reference Fock-space coupled cluster (FSCC) method for predicting molecular hyperfine structure (HFS) constants, including a thorough computational study to estimate the associated uncertainties. In particular, we considered the $^{19}$F HFS constant in the ground and excited states of BaF. Due to a larger basis set dependence, the uncertainties on the excited state results (16-85%) were found to be significantly larger than those on the ground state constants ($\sim$2%). The ab initio values were compared to the recent e…
Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$Na
Physical Research Laboratory（物理研究实验室）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）
We have investigated energies, magnetic dipole hyperfine structure constants ($A_{hyf}$) and electric dipole (E1) matrix elements of a number of low-lying states of the triply ionized tin (Sn$^{3+}$) by employing relativistic coupled-cluster theory. Contributions from the Breit interaction and lower-order quantum electrodynamics (QED) effects in determination of above quantities are also given explicitly. These higher-order relativistic effects are found to be important for accurate evaluation of energies, while QED contributions are seen to be contributing significantly to the determination o…
We measure the hyperfine structure of $nP_{1/2}$ Rydberg states using mm-wave spectroscopy on an ensemble of laser-cooled $^{85}$Rb atoms. Systematic uncertainties in our measurement from the Zeeman splittings induced by stray magnetic fields and dipole-dipole interactions between two Rydberg atoms are factored in with the obtained statistical uncertainty. Our final measurement of the $nP_{1/2}$ hyperfine coupling constant is $A_{\text{hfs}}=1.443(31)$~GHz. This measurement is useful for studies of long-range Rydberg molecules, Rydberg electrometry, and quantum simulation with dipole-dipole in…
Roles of electron correlation effects in the determination of attachment energies, magnetic dipole hyperfine structure constants and electric dipole (E1) matrix elements of the low-lying states in the singly charged cadmium ion (Cd$^+$) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation, second-order many-body perturbation theory and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation…
