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

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.Comment: 16 pages, 7 figures; submitted to Phys. Rev.

Geometry of effective Hamiltonians

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results are hitherto unknown or unpublished. In particular, commuting observables and symmetries are discussed in detail. Simple and explicit proofs are given, and numerical algorithms are proposed, that improve and stabilize common methods used today.Comment: 1 figur

Trans-Rational Cash: Ghost-Money, Hong Kong, and Nonmodern Networks

In this essay, I examine through Bruno Latour's concept of nonmodern networks the intersections of the hyper-modernity of Hong Kong's ‘real’ money economy with that of an economy of ghost-money that, through the act of burning, serves as an offering to the dead and the divine. The essay reconfigures Latour's ‘modern constitution’ as it relates to philosophy, myth and modernity as they are organised around the values of a currency that trespass all boundaries.postprin

Convergence of all-order many-body methods: coupled-cluster study for Li

We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provides a quantitative ground for semi-empirical fits of {\em ab inito} matrix elements to experimental energies.Comment: 4 pages, 3 figure

Automated Microbial Metabolism Laboratory Final report

Automated microbial metabolism life detection experiments for exobiological studie