Charged particles in static electric and magnetic fields have Landau levels and tunneling states from the vacuum. Using the instanton method of Phys. Rev. D 65, 105002 (2002), we obtain the formulas for the pair-production rate in spinor and scalar QED, which sum over all Landau levels and recover exactly the well-known results. The pair-production rates are calculated for an electric field of finite extent, and for the Sauter potential, both with a constant magnetic field also present, and are shown to have finite-size effects.

• Received 21 January 2003

DOI:https://doi.org/10.1103/PhysRevD.73.065020