Wannier threshold law for two-electron escape in the presence of an external electric field

We consider double ionization of atoms or ions by electron impact in the pr esence of a static electric field. As in Wanniers analysis of the analogous situation without external field the dynamics near threshold is dominated by a saddle. With a field the saddle lies in a subspace of symmetrically es caping electrons. Near threshold the classical cross-section scales with ex cess energy E like sigma similar toE(alpha), where the exponent alpha can b e determined from the stability of the saddle and does not depend on the fi eld strength. For example, if the remaining ion has charge Z=2, the exponen t is 1.292, significantly different from the 1.056 without the field.