Superheavy elements and nonlinear electrodynamics

Maxwell's equations, which underlie electrodynamics, are linear equations. Nonlinear effects, such as photon-photon scattering, are known to arise in quantum electrodynamics, and one might expect them to become important in the case of strong external fields. We investigate the consequences of a class of nonlinear Lagrangians, which includes that of Born and Infeld and whose common property is that they lead to upper limits for the electric-field strength (somewhat analogous to the upper limit for the velocity of a particle in special relativity). These nonlinear Lagrangians also lead to a finite electromagnetic selfenergy for the electron, unlike the case of Maxwellian electrodynamics. The importance of nonlinear effects of course depends upon the size of the upper limit to the electric-field strength. If this upper limit is determined by requiring that the mass of the electron is of an entirely electromagnetic origin, nonlinear effects become very important in determining the eigenvalues of electrons bound to superheavy nuclei. For example, the Is energy eigenvalue is raised by 270 keV for Z= 164. The Lagrangians considered here do not lead to an absolute gap between bound states and the states of the lower continuum; the Iδ energy eigenvalue becomes equal to -0.511 MeV, where the lower continuum begins, for Z=215. An analogy between nonlinear electrodynamics and higherorder vacuum polarization corrections is studied.