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arXiv:1706.09640 · Physical Review A

Calculation of the magnetic hyperfine structure constant of alkali metals and alkaline-earth-metal ions using the relativistic coupled-cluster method

Sudip Sasmal

Published Jul 13, 2017• 9 citations
arXivHTMLPDF

Abstract

The $Z$-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant (${A}_{J}$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The $Z$-vector results are in very good agreement with the experiment. The ${A}_{J}$ values of Li, Na, K, Rb, Cs, ${\mathrm{Be}}^{+}$, ${\mathrm{Mg}}^{+}$, ${\mathrm{Ca}}^{+}$, and ${\mathrm{Sr}}^{+}$ obtained in the $Z$-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the $Z$-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.

DOI
10.1103/physreva.96.012510

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The ZZZ-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant (AJ{A}_{J}AJ​) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The ZZZ-vector results are in very good agreement with the experiment. The AJ{A}_{J}AJ​ values of Li, Na, K, Rb, Cs, Be+{\mathrm{Be}}^{+}Be+, Mg+{\mathrm{Mg}}^{+}Mg+, Ca+{\mathrm{Ca}}^{+}Ca+, and Sr+{\mathrm{Sr}}^{+}Sr+ obtained in the ZZZ-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the ZZZ-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.
The molecular dipole moment and magnetic hyperfine-structure constant demand an accurate wave function far from the nucleus and in the near nuclear region, respectively. We, therefore, employ the so-called Z-vector method in the domain of relativistic-coupled-cluster theory to calculate the first-order property of molecular systems in their open-shell ground-state configuration. The implemented method is applied to calculate the molecular dipole moment and parallel component of the magnetic hyperfine-structure constant of the SrF molecule. The results of our calculation are compared with the experimental and other available theoretically calculated values. We are successful in achieving good accordance with the experimental results. The result of our calculation of the molecular dipole moment is in the accuracy of $\ensuremath{\sim}0.5$%, which is clearly an improvement over the previous calculation based on the expectation value method in the four-component coupled-cluster framework [V. S. Prasannaa et al., Phys. Rev. A 90, 052507 (2014)]. Thus, it can be inferred that the Z-vector method can provide an accurate wave function in both the near and far nuclear region, which is evident from our calculated results.
Abstract Using the singles and doubles approximated relativistic coupled-cluster method, we calculate hyperfine-structure constant A and B of 24 low-lying states of La 2+ . The results of the lowest four states 5 d 3/2,5/2 and 4 f 5/2,7/2 are compared with recently measured values (Olmschenk et al 2017 Phys. Rev. A 96 032502). Reasonable agreement is found for hyperfine-structure constant A of 5 d 3/2 and 4 f 5/2,7/2 states, but the hyperfine-structure constant A of 5 d 5/2 and the hyperfine-structure constant B have a large deviation. To understand the role of the electron correlation effect, the intermediate results from lower-order many-body perturbation-theory and the linear version of coupled-cluster with single and double approximation are also presented. In the framework of coupled-cluster theory, the contribution trends from individual correlation effects are also investigated.
Accurate knowledge of interaction potentials among the alkali-metal atoms and alkaline-earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali-metal atoms with the Ca+{\mathrm{Ca}}^{+}Ca+, Ba+{\mathrm{Ba}}^{+}Ba+, Sr+{\mathrm{Sr}}^{+}Sr+, and Ra+{\mathrm{Ra}}^{+}Ra+ alkaline-earth ions systematically, which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above-mentioned systems, which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random-phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representations of the dispersion coefficients versus RRR are given among all the alkaline ions with Rb.
Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in 23^{23}23Na
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We demonstrate an iterative scheme for coupled-cluster property calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline-earth-metal ions are calculated using relativistic coupled-cluster theory and the role of electron correlation is 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.
Ultracold diatomic molecules find application in quantum studies ranging from controlled chemistry and precision measurement physics to quantum many-body simulation and potentially quantum computing. Accurate knowledge of molecular properties is required to guide and explain ongoing experiments. Here, in an extensive and comparative study, we theoretically investigate the electronic properties of the ground-state diatomic molecules composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 78 heteronuclear and homonuclear diatomic combinations, including 21 alkali-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic states, 36 alkali-metal--alkaline-earth-metal molecules in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state, and 21 alkaline-earth-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state. We calculate potential energy curves, permanent electric dipole moments, and polarizabilities using the hierarchy of coupled-cluster methods up to CCSDTQ with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We collect and analyze corresponding spectroscopic constants. We estimate computational uncertainties and compare the present values with previous experimental and theoretical data to establish a different theoretical benchmark. The presented results should be useful for further application of the studied molecules in modern ultracold physics and chemistry experiments.