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Considering an atom at ground state 0.

To be excited to state 1, it needs to get, as understand $E_e = E_0 - E_1$.

What if, atom at $E_0$ interacts with photon, which energy is higher than $E_0 - E_1$, but lower than $E_0 - E_2$?

Will it be elastic or inelastic scattering?

Will the photon just be remitted with different angle and lower wavelength and atom will stay at ground state (elastic scattering), it will be absorbed?

My thoughts

I think it can not be absorbed, because atom can’t be at state, that corresponds that energy (except being at magnetic field, as I know).

It is useful to consider high delta, i.e. receiving not $E_0-E_2 < E > E_0-E_1 $ but $E_0-E_{10} < E > E_0-E_9 $:

I assume, that photon will be scattered, and reradiated with lower energy, and atom will be excited, but for some quasi stationary state with much lower time life.

If it is true, then the question is what will be next? Will it jump from $E_{9.5}$ to ground state, emitting one photon with energy $E_0-E_{9.5}$, or will it jump to 9 stationary state, emitting $E_9 - E_{9.5}$ then to 8, emitting $E_8 - E_9$ and so on?

Some research

In this answer to almost same question I get some confusion: author states, that scattering, where scattered photon has different energy is inelastic, which is logically for me, but Wikipedia, at least Russian states, that both case, when scattered photon changes its wavelength and not — are elastic scattering, and inelastic scattering is when system (atom) changes its internal state or changes number of its particles.

English version of Compton scattering page also states, that it is elastic scattering.

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  • $\begingroup$ Check out the Jaynes-Cummings model which is fully quantum. There is always an amplitude that the photon will be absorbed after a finite time interval. $\endgroup$
    – LPZ
    Mar 24, 2023 at 10:33
  • $\begingroup$ @JohnRennie, as for Your first answer, You mentioned, exactly what I am asking about You characterised as "generally negligable", and that's all, so first one - does not answer my complex question $\endgroup$ Mar 24, 2023 at 17:28
  • $\begingroup$ @JohnRennie, the second's post accepted answer You provided, I mentioned in my question, and I wrote that it is confusing, so it also does not answer my question $\endgroup$ Mar 24, 2023 at 17:30
  • $\begingroup$ @JohnRennie, I think non-accpeted answer is more straight, yet without links and proves $\endgroup$ Mar 24, 2023 at 17:32

1 Answer 1

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Standard Compton scattering is elastic, but the lost photon energy does not have to be restricted to the energy levels of an individual electron. A slight change in energy of the entire atom can occur. Compton scattering is most likely to happen when one electron can absorb and hold the correct amount of energy to keep both momentum and energy conserved. This is why some angles can be much more probable than others.

Also, energy in quantum physics does not have to be conserved all of the time. The energy/time uncertainty principle allows energy to be out of balance for very short periods of time. Scattering at an angle that does not maintain both momentum and energy conservation is less likely but not impossible. It must happen quickly. Any extra energy must be balanced through release of a low energy photon, or perhaps interaction with the nucleus or a nearby atom. Energy does not have to enter only the energy levels of a single electron.

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  • $\begingroup$ Compton scattering is most likely to happen when one electron can absorb and hold the correct amount of energy to keep both momentum and energy conserved” — You still mean elastic scattering in this case? $\endgroup$ Mar 25, 2023 at 8:34

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