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Can someone help me conceptualize the differences between a photon's involvement with absorption, transparency, reflection, and emission?

To be more specific, my current understanding of the matter is that when a photon interacts with an atom containing electrons (not a free electron), if the frequency is high enough, it can be absorbed, and the electron moves to a less-stable, yet higher energy level. In this sense, all other photons that were not absorbed are then reflected back outwards (giving the object its corresponding color). But if the frequency is too low to make the energy gap, the photon passes through the electron cloud and the atoms are transparent in the visual spectrum (as in glass, or air)...

Given this, what is the main ingredient that causes a photon to either be reflected off of the object versus passing straight through it (as in transparency)? As well, when does an emission of the electron get involved (as in, if the electron absorbs a certain frequency, when is a photon emitted versus an electron, and does the electron itself get emitted if it's a valence, or does a separate electron in the sea of electrons elsewhere get emitted to make up for the balance?)

Sorry if it's a bit of a mess; please let me know if my assumptions above are inconsistent, and need tweaking as well before moving forward.

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The physics behind these processes is captured in so-called cross-sections for photon-atom scattering. They can be formulated precisely given the Hamiltonian of the system and evaluated numerically. Important ones are elastic cross-sections, describing the situation where the photon is scattered from the atom but no energy is transferred, excitation cross-sections, where the photon is absorbed leaving the atom in an unstable excited state (which can decay to a state of lower energy emitting a second photon) and ionasation cross-sections, where the photon is absorbed and the atom has gained an energy above its ionisation energy causing it to decay into a positive ion and an electron. The interaction between the electromagnetic field (the photon) and the atom is the same in all cases but the values of the cross-sections depend on the photon energy. Note that although the photon energy may be sufficiently high to cause ionisation the probability for elastic scattering need not be exactly zero. Going beyond these simple processes, if the intensity of a photon beam is sufficiently high but the photon frequencies (i.e., their energy) are too low to cause ionisation then the atom can still be ionised by absorbing more photons (multi-photon ionisation). These processes are experimentally studied using intense laser beams. Here we encounter a cross-section for the process where initially we have an n-photon state (rather than one as above) and an atomic ground state.

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Thanks for the detailed explanation - this definitely helps. –  eeseitz Jun 6 at 14:33
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