Relativistic electron densities in the four-component Dirac representation and in the two-component picture

 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 Schr?dinger 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 ^ν>. The fractional magnitudes of Δ^rel<r ^ν>, of Δ^charge/mass<r ^ν>, 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 Z ²α².