The atomic ionization, capture, and stopping cross sections by multicharged ions satisfy the Benford law

TL;DR

This study investigates whether atomic cross section data and stopping power values follow the Benford law, finding theoretical data conform well while experimental data show less conformity due to limited rank width.

Contribution

The paper demonstrates that theoretical atomic ionization and capture cross sections adhere to the Benford law, providing insights into data distribution patterns in atomic physics.

Findings

Theoretical cross sections satisfy Benford law well.

Experimental stopping power data show limited Benford conformity.

Errors and prime number densities are analyzed and discussed.

Abstract

The applicability of the Benford law for different data sets of atomic cross sections by ion impact is studied. We find that the data sets corresponding to theoretical ionization and capture cross sections of neutral targets by multicharged ions satisfy quite well the Benford law, not only for the first digits but also within a given order of magnitude. Experimental stopping power values from the International Atomic Energy Agency database were also scrutinized, but in this case the Benford conformity was not so satisfactory due to its small rank width. In all cases, errors, densities of prime numbers, and theorems of Nigrini and Pinkham are evaluated and discussed.