Effect of third- and fourth-order moments on the modeling of Unresolved Transition Arrays

TL;DR

This paper explores how third and fourth moments (skewness and kurtosis) influence the statistical modeling of unresolved atomic transition arrays, demonstrating that non-Gaussian distributions can reveal more detailed spectral structures.

Contribution

It introduces the use of Generalized Gaussian distributions constrained by kurtosis for modeling unresolved transition arrays, improving spectral detail representation.

Findings

Non-Gaussian models reveal more detailed spectral structures.

Comparison with detailed calculations validates the new distribution approach.

Analysis of experimental data supports the relevance of the model.

Abstract

The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram-Charlier, Normal Inverse Gaussian and Generalized Gaussian distributions. It is shown that the modeling of unresolved transition arrays with non-Gaussian distributions may reveal more detailed structures, due essentially to the large value of the kurtosis. In the present work, focus is put essentially on the Generalized Gaussian, the power of the argument in the exponential being constrained by the kurtosis value. The relevance of the new statistical line distribution is checked by comparisons with smoothed detailed line-by-line calculations and through the analysis of 2p-3d transitions of recent laser or Z-pinch absorption measurements. The issue of calculating high-order moments is also discussed (Racah algebra, Jucys graphical method, semi-empirical approach ...).