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

In this work, the calculation of a statistical measure of complexity and the FisherShannon information is performed for all the atoms in the periodic table. Nonrelativistic 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 FisherShannon 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.