I read that the photoionization of a ground state hydrogen atom for photon energies $h\nu > I_H$ (where $I_H$ is the ionization energy of $H$ at $13.6 \, \mathrm{eV}$ has a smaller cross section for larger $h\nu$.

Specifically, the photoelectric cross section for a hydrogen atom is approximately,

$$ \sigma_{pe} (\nu) \propto \left(\frac{I_H}{h\nu}\right)^{3}$$

I don't understand this intuitively.

Why does a higher energy photon have a lower cross section of this interaction occurring?

  • $\begingroup$ The father you are from resonance, the weaker you expect the cross section to be in general. This is true even for classical oscillators. $\endgroup$
    – KF Gauss
    Dec 29 '18 at 0:51
  • $\begingroup$ What's the resonance here though? I don't see intuitively why a 20 eV photon has a smaller cross section on ionizing hydrogen than a 14 eV photon. $\endgroup$
    – XYZT
    Dec 29 '18 at 7:08
  • 1
    $\begingroup$ That's a good question, I think the resonance is really to all of the large principle quantum number orbitals (i.e. large n) which in principle can get arbitrarily close to the free electron state. In other words there are a huge number of possible resonances that all live up around 13.6eV. $\endgroup$
    – KF Gauss
    Dec 29 '18 at 7:14

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