An assessment of tunneling-multiphoton dichotomy in atomic photo-ionization: Keldysh parameter versus scaled frequency

It is common practice in strong-laser physics community that dynamical regime of atomic ionization is described by the Keldysh parameter, $\gamma$. Two distinct cases where $\gamma\ll 1$ and $\gamma\gg 1$ are associated with ionization mechanisms that are predominantly in tunneling and in multi-photon regimes, respectively. We report on our fully three-dimensional {\it ab initio} quantum simulations of ionization of hydrogen atoms in laser fields described in terms of the Keldysh parameter by solving the corresponding time-dependent Schr\"odinger equation. We find that the Keldysh parameter is useful in inferring the dynamical ionization regime only when coupled with the scaled laser frequency, $\Omega$, when a large range of laser frequencies and peak intensities are considered. The additional parameter $\Omega$ relates the laser frequency $\omega$ to the classical Kepler frequency $\omega_K$ of the electron, and together with the Keldysh parameter, they can be used to refer to an ionization regime.