Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high atomic number Z

The motion of circular wave packets for one electron in a central Coulomb field with a high atomic number Z is calculated. The wave packet is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects, in particular the spin-orbit potential. A time scale is defined within which spin dynamics must be taken into account, mainly in atoms with high Z. Within this time scale there exists a mechanism of collapses and revivals of the spin, already shown by the authors for harmonic oscillator potential and called the spin-orbit pendulum. Though this effect does not have the exact periodicity of the simpler model, the wave packet spatial motion is nevertheless quite similar.