Characterization of anomalous Zeeman patterns in complex atomic spectra

TL;DR

This paper introduces a statistical method to analyze complex atomic spectra affected by magnetic fields, improving efficiency over previous approaches by using moments and Hermite polynomial expansions.

Contribution

The paper presents a novel statistical approach using moments and Hermite polynomials to model Zeeman profiles, offering better convergence than traditional Taylor-series methods.

Findings

Efficient modeling of Zeeman profiles using moments and Hermite polynomials.

A new approximate method to estimate magnetic field effects on spectral line widths.

Validation showing improved convergence and broader validity range.

Abstract

The modeling of complex atomic spectra is a difficult task, due to the huge number of levels and lines involved. In the presence of a magnetic field, the computation becomes even more difficult. The anomalous Zeeman pattern is a superposition of many absorption or emission profiles with different Zeeman relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a statistical approach to study the effect of a magnetic field on the broadening of spectral lines and transition arrays in atomic spectra. In this model, the sigma and pi profiles are described using the moments of the Zeeman components, which depend on quantum numbers and Land\'{e} factors. A graphical calculation of these moments, together with a statistical modeling of Zeeman profiles as expansions in terms of Hermite polynomials are presented. It is shown that the procedure is more efficient, in terms of convergence and validity range, than the Taylor-series expansion in powers of the magnetic field which was suggested in the past. Finally, a simple approximate method to estimate the contribution of a magnetic field to the width of transition arrays is proposed. It relies on our recently published recursive technique for the numbering of LS-terms of an arbitrary configuration.