dorsal/arxiv
View Schema"Dressing" lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties
| Authors | Andrei Derevianko, Sergey Porsev |
|---|---|
| Categories | |
| ArXiv ID | physics/0410012 |
| URL | https://arxiv.org/abs/physics/0410012 |
| DOI | 10.1103/PhysRevA.71.032509 |
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 $C^\dagger C$ 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.
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"abstract": "We consider evaluation of matrix elements with the coupled-cluster method.\nSuch calculations formally involve infinite number of terms and we devise a\nmethod of partial summation (dressing) of the resulting series. Our formalism\nis built upon an expansion of the product $C^\\dagger C$ of cluster amplitudes\n$C$ into a sum of $n$-body insertions. We consider two types of insertions:\nparticle/hole line insertion and two-particle/two-hole\nrandom-phase-approximation-like insertion. We demonstrate how to ``dress\u0027\u0027\nthese insertions and formulate iterative equations. We illustrate the dressing\nequations in the case when the cluster operator is truncated at single and\ndouble excitations. Using univalent systems as an example, we upgrade\ncoupled-cluster diagrams for matrix elements with the dressed insertions and\nhighlight a relation to pertinent fourth-order diagrams. We illustrate our\nformalism with relativistic calculations of hyperfine constant $A(6s)$ and\n$6s_{1/2}-6p_{1/2}$ electric-dipole transition amplitude for Cs atom. Finally,\nwe augment the truncated coupled-cluster calculations with otherwise omitted\nfourth-order diagrams. The resulting analysis for Cs is complete through the\nfourth-order of many-body perturbation theory and reveals an important role of\ntriple and disconnected quadruple excitations.",
"arxiv_id": "physics/0410012",
"authors": [
"Andrei Derevianko",
"Sergey Porsev"
],
"categories": [
"physics.atom-ph",
"physics.chem-ph"
],
"doi": "10.1103/PhysRevA.71.032509",
"title": "\"Dressing\" lines and vertices in calculations of matrix elements with the coupled-cluster method and determination of Cs atomic properties",
"url": "https://arxiv.org/abs/physics/0410012"
},
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