Benford's law and complex atomic spectra

TL;DR

This paper demonstrates that the strengths of electric-dipolar lines in complex atomic spectra follow Benford's law, revealing underlying statistical properties and offering a new test for spectroscopic models.

Contribution

It shows that atomic spectra line strengths obey Benford's law and links this to random matrix theory and Porter-Thomas law, providing a novel perspective on atomic spectra statistics.

Findings

Line strengths follow Benford's law.

Benford's law reflects uncorrelated probability laws.

Applicable as a test for spectroscopic models.

Abstract

We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This indicates that atomic processes result from the superposition of uncorrelated probability laws and that the occurrence of digits reflects the constraints induced by the selection rules. Furthermore, Benford's law can be a useful test of theoretical spectroscopic models. Its applicability to the statistics of electric-dipolar lines can be understood in the framework of random matrix theory and is consistent with the Porter-Thomas law.