Dichotomy between tunneling and multiphoton ionization in atomic photoionization: Keldysh parameter γ versus scaled frequency Ω

It is commonly accepted in the strong-laser physics community that the dynamical regime of atomic ionization is characterized by the Keldysh parameter γ. Two distinct cases, where γ<1 and γ>1, are associated with ionization mechanisms that are predominantly in the tunneling and in the multiphoton regimes, respectively. We perform fully three-dimensional quantum simulations for the ionization of the hydrogen atom by solving the time-dependent Schr\"odinger equation for a wide range of laser parameters encoded by the Keldysh parameter. We find that the meaning of the Keldysh parameter γ changes when the laser frequency ω is changed, and demonstrate that γ is useful in determining the dynamical ionization regime only when coupled with the scaled laser frequency Ω when a large range of laser frequencies and peak intensities are considered. The scaled frequency Ω relates the laser frequency ω to the classical Kepler frequency ωK of the bound electron. Together with the Keldysh parameter, the pair (γ,Ω) refers to a more realistic picture of the dynamical ionization regime. We refer to final momentum distributions of the ionized electrons at several interesting points on the (γ,Ω) landscape in order to infer whether the tunneling or the multiphoton mechanism is dominant in these regions.