Alternative evaluation of statistical indicators in atoms: the non-relativistic and relativistic cases

TL;DR

This study calculates statistical complexity and Fisher-Shannon information for all atoms, considering non-relativistic and relativistic effects, revealing shell structures and irregularities through these measures.

Contribution

It introduces an alternative method using fractional occupation probabilities to evaluate atomic complexity and information measures, incorporating relativistic effects.

Findings

Both measures increase with atomic number Z.

Shell structure is clearly displayed by Fisher-Shannon information.

Relativistic effects influence the information measures.

Abstract

In this work, the calculation of a statistical measure of complexity and the Fisher-Shannon information is performed for all the atoms in the periodic table. Non-relativistic and relativistic cases are considered. We follow the method suggested in [C.P. Panos, N.S. Nikolaidis, K. Ch. Chatzisavvas, C.C. Tsouros, arXiv:0812.3963v1] that uses the fractional occupation probabilities of electrons in atomic orbitals, instead of the continuous electronic wave functions. For the order of shell filling in the relativistic case, we take into account the effect due to electronic spin-orbit interaction. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the atomic number $Z$ is observed. The shell structure and the irregular shell filling is well displayed by the Fisher-Shannon information in the relativistic case.