Relativistic electron densities in the four-component Dirac representation and in the two-component picture: Hydrogen-like systems

Analytic formulae of the relativistic radial functions of hydrogen-like atoms in the four-component standard Dirac picture and in two approximations, (Pauli and ZORA), to the two-component (so-called Schrödinger or Newton-Wigner) picture and graphs of the respective relativistic changes of densities are presented and discussed. The two different pictures of the Dirac density of charge position and of the Newton-Wigner density of mass position are remarkably different in strongly inhomogeneous fields and result in respective differences in position-dependent expectation values. 〈r^v〉. The fractional magnitudes of Δ^rcl〈r^v〉, of Δ^charge/mass〈r^v〉, and of the gauge dependence of ZORA (which for small n states is comparable to the difference of the two kinds of position observables) are all of order Z²a².