Keldysh ionization theory of atoms: mathematical details

Abstract

Abstract Keldysh ionization theory is one of the main pillars of strong field physics and attosecond science. It describes non-relativistic ionization rates of hydrogen-like atoms subjected to strong laser fields within the dipole approximation and the length gauge. According to this theory ionization can be described by two regimes: electronic tunneling through a laser-dressed atomic potential (tunnel ionization) and absorption of multiple photons at once (multi-photon ionization). There are many gaps in the mathematical steps and explanations in the original Keldysh paper. Therefore, the goal of this work is to give a detailed re-derivation of ionization rates following Keldysh’s formulation and to fill in the mathematical steps of this beautiful approach so that it is more accessible to a wider audience.