"Dressing" lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties

Abstract

We consider evaluation of matrix elements with the coupled-cluster method. Such calculations formally involve infinite number of terms and we devise a method of partial summation (dressing) of the resulting series. Our formalism is built upon an expansion of the product $C^{†}C$ of cluster amplitudes $C$ 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 hyperfine constant $A(6s)$ and $6s_{1/2}-6p_{1/2}$ electric-dipole transition amplitude for 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.

16 pages, 7 figures; submitted to Phys. Rev. A

References in corpus (5)

• Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements and static polarizabilities for alkali-metal atoms
• High precision measurement of the static dipole polarizability of cesium
• Correlated many-body treatment of Breit interaction with application to cesium atomic properties and parity violation
• Fourth-order perturbative extension of the singles-doubles coupled-cluster method
• Reevaluation of the role of nuclear uncertainties in experiments on atomic parity violation with isotopic chains

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• Theoretical overview of atomic parity violation. Recent developments and challenges
• Convergence of all-order many-body methods: coupled-cluster study for Li
• Precision theoretical determination of electric-dipole matrix elements in atomic cesium
• Parity-mixed coupled-cluster formalism for computing parity-violating amplitudes
• Coupled-cluster calculations of properties of Boron atom as a monovalent system
• Role of triple excitations in calculating different properties of Ba+
• Development of algebraic techniques for the atomic open-shell MBPT(3)