Statistics of electric-quadrupole lines in atomic spectra

TL;DR

This paper develops analytical formulas and statistical tools to estimate and analyze electric-quadrupole (E2) lines in atomic spectra, especially relevant for hot plasmas with highly stripped ions.

Contribution

It introduces new analytical formulas and a generalized sum rule for E2 lines, enhancing the understanding of multipole transitions in atomic spectra.

Findings

Formulas for estimating the number of E2 lines in transition arrays

A generalized 'J-file' sum rule for E2 lines

Statistical descriptions of line energies including shift and variance

Abstract

In hot plasmas, a temperature of a few tens of eV is sufficient for producing highly stripped ions where multipole transitions become important. At low density, the transitions from tightly bound inner shells lead to electric-quadrupole (E2) lines which are comparable in strength with electric-dipole ones. In this work, we propose analytical formulas for the estimation of the number of E2 lines in a transition array. Such expressions rely on statistical descriptions of electron states and J-levels. A generalized 'J-file' sum rule for E2 lines and the strength-weighted shift and variance of the line energies of a transition array nl^N+1 \rightarrow nl^Nn'l' of inter-configuration E2 lines are also presented.