arXiv:1009.2963 · Physical Review A

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

Brajesh Kumar Mani, D. Angom

Published Jan 7, 2011• 27 citations

Abstract

We have developed an all-particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine structure constants, and electric dipole matrix elements of Sr, Ba, and Yb. Furthermore, we calculate the electric quadrupole hyperfine structure constants and the electric dipole matrix elements of ${\mathrm{Sr}}^{+}$, ${\mathrm{Ba}}^{+}$, 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 ${\mathrm{Yb}}^{+}$.

DOI: 10.1103/physreva.83.012501

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arXiv:1009.2963 · Physical Review A

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

Brajesh Kumar Mani, D. Angom

Published Jan 7, 2011• 27 citations

arXiv HTML PDF

Abstract

{\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}}^{+}

DOI: 10.1103/physreva.83.012501

Related papers

Role of triple excitations in calculating different properties of Ba+

S. G. Porsev, Marianna S. Safronova

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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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.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.

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

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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.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.

arXiv:1706.09640Physical Review AJul 13, 20179 citations

{\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}}^{+}

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.

Triple excitation in relativistic coupled-cluster theory and properties of one-valence systems Rb and Sr

^+

^+

are analysed using the perturbed triples.

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.