Filling gap of combination of gauge and analytical method in KFR-like theory

Bauer recently presented a formula for the ionization rate of a hydrogen atom in a strong linearly polarized laser field J. Phys. B 49 145601 (2016). He started from the Keldysh probability amplitude in the length gauge and utilized Reiss's method in the velocity gauge. Instead, according to the Reiss probability amplitude in the velocity gauge and Keldysh's derivation for the length gauge, we derive a formula for the ionization rate of a ground-state hydrogen atom or a hydrogen-like atom in a strong linearly polarized laser field. We compare the numerical results of the total ionization rate and the photoelectron energy distribution calculated from our formula with the results from Keldysh, Reiss, and Bauer. We find that the apparent discrepancies in the ionization rate are caused not only by different gauges, but also by different analytical methods used to derive the ionization rate.