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

TL;DR

This paper investigates the convergence behavior of all-order coupled-cluster methods applied to lithium, providing insights into high-order many-body contributions and their scaling, which aids in improving ab initio calculations.

Contribution

It offers a comprehensive relativistic coupled-cluster analysis of Li, including high-order contributions and their scaling, enhancing understanding of convergence in many-body methods.

Findings

High-order contributions scale proportionally for energies and matrix elements.

Nearly complete many-body calculations enable analysis of convergence patterns.

Results support semi-empirical fitting of ab initio matrix elements to experimental data.

Abstract

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.