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 presence 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 escaping electrons. Near threshold the classical cross section scales with excess energy E like sigma=E^alpha, where the exponent alpha can be determined from the stability of the saddle and does not depend on the field strength. For example, if the remaining ion has charge Z=2, the exponent is 1.292, significantly different from the 1.056 without the field.