arXiv:0912.3681 · Physical Review A

Atomic properties calculated by relativistic coupled-cluster theory without truncation: Hyperfine constants of Mg+ , Ca+ , Sr+ , and Ba+

Brajesh Kumar Mani, D. Angom

Published Apr 20, 2010• 33 citations

Abstract

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.

DOI: 10.1103/physreva.81.042514

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arXiv:0912.3681 · Physical Review A

Atomic properties calculated by relativistic coupled-cluster theory without truncation: Hyperfine constants of Mg+ , Ca+ , Sr+ , and Ba+

Brajesh Kumar Mani, D. Angom

Published Apr 20, 2010• 33 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.81.042514

Related papers

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

Sudip Sasmal

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.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.

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Fock-space relativistic coupled-cluster calculations of two-valence atoms

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We carried out calculations of the energies, hyperfine structure constants, and electric-dipole transition amplitudes for the low-lying states of ${\mathrm{Ba}}^{+}$ in the framework of the relativistic linearized coupled-cluster single double and coupled-cluster single double (valence) triple methods. Taking into account that an iterative inclusion of the valence triples into consideration is a complicated and computationally demanding process, we study the effects of computational restriction on the final results. We also present a detailed study of various corrections to all calculated properties, and we use our results to formulate several broad rules that can be used in future calculations of the elements where experimental data are scarce and correct theoretical predictions are highly important.We carried out calculations of the energies, hyperfine structure constants, and electric-dipole transition amplitudes for the low-lying states of ${\mathrm{Ba}}^{+}$ in the framework of the relativistic linearized coupled-cluster single double and coupled-cluster single double (valence) triple methods. Taking into account that an iterative inclusion of the valence triples into consideration is a complicated and computationally demanding process, we study the effects of computational restriction on the final results. We also present a detailed study of various corrections to all calculated properties, and we use our results to formulate several broad rules that can be used in future calculations of the elements where experimental data are scarce and correct theoretical predictions are highly important.

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Accurate determination of hyperfine structure constants in atomic systems provides important insight into the interplay of electron correlation and relativistic effects in the nuclear region. Although sodium (Na) is a relatively light atom, previous all-order relativistic many-body calculations of the magnetic dipole hyperfine constants for the low-lying states of $^{23}$ Na show noticeable discrepancies with experiment. To address this, we calculate the ionization potentials and hyperfine structure constants of $^{23}$ Na using relativistic coupled-cluster theory with explicit inclusion of triple excitations. We further incorporate corrections from the Breit interaction, quantum electrodynamics, and the Bohr-Weisskopf (BW) effect. Results from lower-order methods are also presented to assess the importance of different physical contributions across states. Our calculations demonstrate that contributions from the lower-order relativistic and BW effects play almost similar roles with the electron correlation effects, including triple excitations, and are essential for reconciling theoretical predictions with experimental observations. This study can also serve as a useful guide for understanding the role of triples in heavier alkali systems.Accurate determination of hyperfine structure constants in atomic systems provides important insight into the interplay of electron correlation and relativistic effects in the nuclear region. Although sodium (Na) is a relatively light atom, previous all-order relativistic many-body calculations of the magnetic dipole hyperfine constants for the low-lying states of $^{23}$Na show noticeable discrepancies with experiment. To address this, we calculate the ionization potentials and hyperfine structure constants of $^{23}$Na using relativistic coupled-cluster theory with explicit inclusion of triple excitations. We further incorporate corrections from the Breit interaction, quantum electrodynamics, and the Bohr-Weisskopf (BW) effect. Results from lower-order methods are also presented to assess the importance of different physical contributions across states. Our calculations demonstrate that contributions from the lower-order relativistic and BW effects play almost similar roles with the electron correlation effects, including triple excitations, and are essential for reconciling theoretical predictions with experimental observations. This study can also serve as a useful guide for understanding the role of triples in heavier alkali systems.

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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.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.

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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.

{\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}}^{+}

C

into a sum of

n

-body insertions. We consider two types of insertions: particle (hole) line insertion and two-particle (two-hole) random-phase-approximation-like insertion. We demonstrate how to ``dress'' these insertions and formulate iterative equations. We illustrate the dressing equations in the case when the cluster operator is truncated at single and double excitations. Using univalent systems as an example, we upgrade coupled-cluster diagrams for matrix elements with the dressed insertions and highlight a relation to pertinent fourth-order diagrams. We illustrate our formalism with relativistic calculations of the hyperfine constant

A(6s)

and the $6{s}_{1∕2}\ensuremath{-}6{p}_{1∕2}$ electric-dipole transition amplitude for the Cs atom. Finally, we augment the truncated coupled-cluster calculations with otherwise omitted fourth order diagrams. The resulting analysis for Cs is complete through the fourth order of many-body perturbation theory and reveals an important role of triple and disconnected quadruple excitations.

We carried out calculations of the energies, hyperfine structure constants, and electric-dipole transition amplitudes for the low-lying states of

{\mathrm{Ba}}^{+}

in the framework of the relativistic linearized coupled-cluster single double and coupled-cluster single double (valence) triple methods. Taking into account that an iterative inclusion of the valence triples into consideration is a complicated and computationally demanding process, we study the effects of computational restriction on the final results. We also present a detailed study of various corrections to all calculated properties, and we use our results to formulate several broad rules that can be used in future calculations of the elements where experimental data are scarce and correct theoretical predictions are highly important.

Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in

^{23}

^{23}

Na show noticeable discrepancies with experiment. To address this, we calculate the ionization potentials and hyperfine structure constants of

^{23}

Na using relativistic coupled-cluster theory with explicit inclusion of triple excitations. We further incorporate corrections from the Breit interaction, quantum electrodynamics, and the Bohr-Weisskopf (BW) effect. Results from lower-order methods are also presented to assess the importance of different physical contributions across states. Our calculations demonstrate that contributions from the lower-order relativistic and BW effects play almost similar roles with the electron correlation effects, including triple excitations, and are essential for reconciling theoretical predictions with experimental observations. This study can also serve as a useful guide for understanding the role of triples in heavier alkali systems.