Relativistic global and local divergences in hydrogenic systems: A study in position and momentum spaces

Abstract

Relativistic effects in one-particle densities of hydrogenic systems are quantified by means of global and local density functionals: the Jensen-Shannon and the Jensen-Fisher divergences, respectively. The Schr\"odinger and Dirac radial densities are compared, providing complementary results in position and momentum spaces. While the electron cloud gets compressed towards the origin in the Dirac case, the momentum density spreads out over its domain, and the raising of minima in position space does not occur in the momentum space. Regarding the dependence on the nuclear charge and the state quantum numbers for all divergences here considered, as well as their mutual interconnection, accurate powerlike laws $y\ensuremath{\approx}C{x}^{a}$ are found systematically. The parameters ${C,a}$ defining the respective dependences are extremely sensitive to the closeness of the system to the ground and/or the circular state. Particularly interesting are the analyses of (i) the plane subtended by the Jensen-Shannon and Jensen-Fisher divergences, in a given space (position or momentum), and (ii) either of the above two divergences in the position-momentum plane. These kinds of results show the complementary role of global and local divergences and that of both conjugate spaces.