\mu m}])^2
  \quad ,
\label{eq_U_pond}\end{aligned}$$ where $\lambda_\mathrm{las}$ is the photon wavelength. The other aspect concerns the electronic binding in the system, which can be quantified by the ionization potential (IP) with associated energy $E_\mathrm{IP}$. What counts is the relation between $E_\mathrm{IP}$ an $U_p$, quantified by the Keldysh parameter [@Kel64] : $$\gamma
  =
  \sqrt{\frac{E_\mathrm{IP}}{2U_p}}
  =
  \sqrt{\frac{2\, E_\mathrm{IP}\, \omega_\mathrm{las}^2}{I_0}}
  \quad.
  \label{eq:Keldysh}$$ The value $\gamma = 1$ (see Fig. \[fig:laser-regimes\] in the case $E_\mathrm{IP}=1$ eV) separates two regimes. For $\gamma\ll 1$, direct ionization (over barrier or tunneling) prevails. This regime is dominated by laser intensity and not so much by laser frequency (field-dominated regime). For $\gamma\gg 1$, emission proceeds through multi-photon ionization in a regime of weak perturbations. There, the results sensitively depend on laser frequency (photon- or frequency-dominated regime).

### Not on lasers: collisions with fast ions {#sec:ioncoll}

There is an alternative excitation mechanism by collisions with charged projectiles. We shall also marginally consider a few examples of collisions with fast ions and thus comment briefly about this tool here. Experiments with charged, fast ions often require access to large scale facilities. Thus there are much less experiments with irradiation by charged projectiles than by the more easily accessible and versatile lasers. 