Complexity analysis of Klein-Gordon single-particle systems

TL;DR

This paper uses Fisher-Shannon complexity to quantify relativistic effects on the internal disorder of Klein-Gordon Coulomb systems, revealing dependence on nuclear charge and quantum numbers, especially in pionic atoms.

Contribution

It introduces a complexity-based approach to analyze relativistic effects in Klein-Gordon systems, highlighting the influence of potential strength and quantum states.

Findings

Fisher-Shannon complexity depends on nuclear charge in relativistic systems.

Relativistic effects increase as quantum numbers n and l decrease.

Complexity variation is illustrated for pionic atoms.

Abstract

The Fisher-Shannon complexity is used to quantitatively estimate the contribution of relativistic effects to on the internal disorder of Klein-Gordon single-particle Coulomb systems which is manifest in the rich variety of three-dimensional geometries of its corresponding quantum-mechanical probability density. It is observed that, contrary to the non-relativistic case, the Fisher-Shannon complexity of these relativistic systems does depend on the potential strength (nuclear charge). This is numerically illustrated for pionic atoms. Moreover, its variation with the quantum numbers (n, l, m) is analysed in various ground and excited states. It is found that the relativistic effects enhance when n and/or l are decreasing.