Atomic ionization, capture, and stopping cross sections by ion impact examined with the Benford law

Abstract

Cross-section databases for atomic ionization, capture, and stopping by ion impact are intensively used in different areas of basic research, as well as in technological developments. We propose examining these databases by using the Benford law. In this chapter, the applicability of the Benford law for given data sets of theoretical and experimental atomic cross sections by ion impact is studied. We found that the data sets corresponding to theoretical ionization, capture, and stopping cross sections 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 the cases, densities of prime numbers and theorems of Nigrini and Pinkham are evaluated and discussed. Furthermore, we introduce different relative errors which represent useful tools to test atomic databases in general.