Ionization in an intense field considering Coulomb correction

We derive a simple ionization rate formula for the ground state of a hydrogen atom in the velocity gauge under the conditions: ω<<1 a.u. (a.u. is short for atomic unit) and γ<<1 (ω is the laser frequency and γ is the Keldysh parameter). Comparisons are made among the different versions of the Keldysh-Faisal-Reiss (KFR) theory. The numerical study shows that with considering the quasi-classical (WKB) Coulomb correction in the final state of the ionized electron, the photoionization rate is enhanced compared with without considering the Coulomb correction, and the Reiss theory with the WKB Coulomb correction gives the correct result in the tunneling regime. Our concise formula of the ionization rate may provide an insight into the ionization mechanism for the ground state of a hydrogen atom.