Benford's law in atomic spectra and opacity databases

TL;DR

This study investigates whether atomic spectra and opacity data from NIST databases follow Benford's law, revealing that digit distribution aligns with the law and can help identify inconsistencies in atomic data.

Contribution

It demonstrates that atomic spectral and opacity data adhere to Benford's law, suggesting a new method for detecting inconsistencies in atomic databases.

Findings

Atomic data follow Benford's law with high accuracy.

Digit distribution reflects atomic process constraints.

Benford's law can identify database inconsistencies.

Abstract

The intriguing law of anomalous numbers, also named Benford's law, states that the significant digits of data follow a logarithmic distribution favoring the smallest values. In this work, we test the compliance with this law of the atomic databases developed at the National Institute of Standards and Technology (NIST) focusing on line energies, oscillator strengths, Einstein coefficients and radiative opacities. The considered databases are the Atomic Spectra Database (ASD) and the NIST-LANL (Los Alamos National Laboratory) Lanthanide/Actinide Opacity Database. The present study is not limited to the first digit and the case of multipole lines is also considered. The fact that the law is verified with a high accuracy means that the occurrence of digits reflects the constraints induced, in a given angular-momentum coupling, by the selection rules for atomic processes. As a consequence, Benford's law may be of great interest to detect inconsistencies in atomic databases.