arXiv:1109.6912

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

Brajesh Kumar Mani, D. Angom

Published Sep 30, 2011• 0 citations

Abstract

We examine the contributions from triple excitation cluster operators in the relativistic coupled-cluster theory in atoms and ions. For this, we propose a tensor representation of the triple cluster operator. Based on this representaion and using diagrammatic analysis, we derive the linearized coupled-cluster equations for single, double and triple excitation cluster operators. The contributions from the triple cluster operators to the hyper fine structure constants of single-valence systems Rb and Sr$^+$ are analysed using the perturbed triples.

DOI: 10.48550/arxiv.1109.6912

Related papers

Role of triple excitations in calculating different properties of Ba+

S. G. Porsev, Marianna S. Safronova

arXiv:2103.02776Physical Review AApr 19, 20216 citations

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

Brajesh Kumar Mani, D. Angom

arXiv:1009.2963Physical Review AJan 7, 201127 citations

Fourth-order perturbative extension of the single-double excitation coupled-cluster method

Andrei Derevianko, Erik D. Emmons

arXiv:physics/0204056Physical Review AJul 15, 200231 citations

Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$Na

Vaibhav Katyal, B. K. Sahoo

physics.atom-phCross-listedarXiv:2607.05012Jul 7, 2026

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

Brajesh Kumar Mani, D. Angom

arXiv:0912.3681Physical Review AApr 20, 201033 citations

Calculation of fine-structure splittings in high-lying F2 states of rubidium

Steven A. Blundell

Physical Review AOct 31, 20147 citations

arXiv:1109.6912

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

Brajesh Kumar Mani, D. Angom

Published Sep 30, 2011• 0 citations

arXiv HTML PDF

Abstract

^+

are analysed using the perturbed triples.

DOI: 10.48550/arxiv.1109.6912

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.

arXiv:2103.02776Physical Review AApr 19, 20216 citations

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

Brajesh Kumar Mani, D. Angom

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 ${\mathrm{Yb}}^{+}$ .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 ${\mathrm{Yb}}^{+}$.

arXiv:1009.2963Physical Review AJan 7, 201127 citations

Fourth-order perturbative extension of the single-double excitation coupled-cluster method

Andrei Derevianko, Erik D. Emmons

Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed.Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed.

arXiv:physics/0204056Physical Review AJul 15, 200231 citations

Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$ NaInvestigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$Na

Vaibhav Katyal, B. K. Sahoo

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.

physics.atom-phCross-listedarXiv:2607.05012Jul 7, 2026

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

Brajesh Kumar Mani, D. Angom

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.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.

arXiv:0912.3681Physical Review AApr 20, 201033 citations

Calculation of fine-structure splittings in high-lying F2 states of rubidium

Steven A. Blundell

We present relativistic many-body calculations of the fine-structure splittings of the $n\phantom{\rule{0.16em}{0ex}}{}^{2}F$ Rydberg states of Rb $(n=4$ --16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the $^{2}\mathrm{F}$ states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.We present relativistic many-body calculations of the fine-structure splittings of the $n\phantom{\rule{0.16em}{0ex}}{}^{2}F$ Rydberg states of Rb $(n=4$--16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the $^{2}\mathrm{F}$ states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.

Physical Review AOct 31, 20147 citations

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

^+

^+

are analysed using the perturbed triples.

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.

{\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}}^{+}

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.

We present relativistic many-body calculations of the fine-structure splittings of the

n\phantom{\rule{0.16em}{0ex}}{}^{2}F

Rydberg states of Rb

(n=4

--16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the

^{2}\mathrm{F}

states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.