Can an electron which is a bound in an atom absorb more than one photon at the same time ? In specific during photo-electric emission can an electron take in more than one photon if one photon doesn't give it the energy required to drift away from the atom
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One should keep in mind that it is the system "electron+nucleus " that absorbs the photon(s). – anna v Mar 03 '15 at 12:03
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Yes, this is actually often used in a spectroscopic technique called REMPI -- see the image on this wikipedia page https://en.wikipedia.org/wiki/Resonance-enhanced_multiphoton_ionization
There are some important physics techniques that rely on interaction with two photons -- two photon spectroscopy (http://cua.mit.edu/8.421_S06/Chapter9.pdf).
Some other techniques, like Raman spectroscopy, involve interaction with two photons (but one absorbed, one emitted).
Gremlin
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And multi-photon ionisation can occur where such a number of photons is absorbed from an intense laser source that enough energy is available for removal of the electron from the remaining ion, see https://en.wikipedia.org/wiki/Photoionization#Multi-photon_ionization – Urgje Mar 03 '15 at 18:30