Endpoint contribution to the instantaneous ionization rate for tunneling ionization

Abstract

We examine the instantaneous ionization amplitudes and instantaneous ionization rates for the process of tunneling ionization. We show that the endpoint contribution usually neglected in the asymptotic evaluation of the amplitudes, may be significant. For weak fields the instantaneous ionization rate is largely defined by this contribution. For higher field strengths of the order of 0.1 a.u., the account of this contribution allows one to reproduce numerically computed instantaneous ionization rates with higher accuracy