Relativistic precession and spin dynamics of an elliptic Rydberg wave packet

The time evolution of wave packets (WPs) built from the eigenstates of the Dirac equation for a hydrogenic system is considered. We investigate the space and spin motion of wave packets which, in the non-relativistic limit, are stationary states with a probability density distributed almost uniformly along the classical, elliptical orbit (elliptic WP). We show that the precession of such a WP, due to relativistic corrections to the energy eigenvalues, is strongly correlated with the spin motion. We also show that the motion is universal for all hydrogenic systems with an arbitrary value of the atomic number Z.