Relaxation effect and radiative corrections in many-electron atoms

We illuminate the importance of a self-consistent many-body treatment in calculations of vacuum polarization corrections to the energies of atomic orbitals in many-electron atoms. Including vacuum polarization in the atomic Hamiltonian causes a readjustment (relaxation) of the electrostatic self-consistent field. The induced change in the electrostatic energies is substantial for states with the orbital angular momentum $l>0$. For such orbitals, the relaxation mechanism determines the sign and even the order of magnitude of the total vacuum polarization correction. This relaxation mechanism is illustrated with numerical results for the Cs atom.

Figure 1

Uehling potential for ${}^{133}\mathrm{Cs}$. Notice that the radius of the innermost $1s$ orbital is about ${10}^3\text{fm}$, much larger than the effective range of the VP potential.

Figure 2

Perturbation of the electronic radial charge distribution $\delta {\rho }_{\text{el}}\left(r\right)$ (solid line) for the Cs atom due to vacuum polarization by the nucleus. We also show the unperturbed density ${\rho }_{\text{el}}\left(r\right)$ multiplied by a factor of ${10}^{-3}$ (dashed line). The minima of ${\rho }_{\text{el}}\left(r\right)$ correspond to positions of the electronic shells, marked on the plot by their values of the principal quantum number $n$.