What actually happens when a photon strikes an atom?

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I know that when a photon strikes an atom, it excites an electron, which then will re-emit the photon when it returns to normal. But what is actually happening here? Is it really as simple as that, or is there something more fundamental going on here, like how nuclei are bound together using carrier particles?
 
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Low-energy photons interact with the atomic electrons and their energy levels, basically like you described. This usually means visible or near-visible (infrared or ultraviolet). With heavier atoms you can also get this sort of interaction using X-ray photons. The nucleus basically doesn't come into play except in the sense that its attraction of the electrons (inserted into Schrödinger's equation) creates the discrete energy levels. Differences in shape or spin of the nucleus can cause very small effects on the electron energy levels. Look up "fine structure" and "hyperfine structure" in atomic spectra.

High-energy photons such as in gamma rays can interact directly with the nucleus, in which case the electrons are not involved.