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Benford's law in atomic spectra and opacity databases



Yuri Ralchenko, Jean-Christophe Pain


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 atomic processes result from the superposition of uncorrelated probability laws and that the occurrence of digits reflects the constraints induced by the selection rules. As a consequence, Benford's law is of great interest to detect errors in atomic databases
Journal of Quantitative Spectroscopy and Radiative Transfer


Atomic databases, opacity databases, atomic spectroscopy, Benford's law


Ralchenko, Y. and Pain, J. (2024), Benford's law in atomic spectra and opacity databases, Journal of Quantitative Spectroscopy and Radiative Transfer, [online],, (Accessed June 17, 2024)


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Created April 21, 2024, Updated May 15, 2024