I have tried to find references for numbers on the two-photon ionization of H and He, i.e. ionization via photons of energies lower than the ionization energy.

My goal is to decide whether natural light sources (mainly young stars) can provide enough intensity for the two-photon processes to be important in hot exoplanetary atmospheres. Typical, but high fluxes in the wavelength region between 90nm and 400nm are $10^6-10^7 \; erg\; cm^{-2}\; s^{-1}$, corresponding to $1 W/cm^2$. From what I see in papers, this is probably >10 orders of magnitude too low, but I wanted someone more knowledgeable to comment on this.



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