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Since an absorption of one photon by two electrons was experimentally noticed when one photon excites two atoms in touch, should we accept even an emission in common of one photon by two electrons?

Sava
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    I'm not sure I understand what you are referring to. Can you provide some link or reference, or explain better? – glS Jan 24 '15 at 11:33
  • I also don't understand. An isolated electron emits only when it is accelerated. Anyway, would you give us the reference for "absorption of one photon by two electrons was experimentally noticed" ? It is not the electrons that absorb the photons, it is the atoms. – Sofia Jan 24 '15 at 11:41
  • @Sofia we generally consider the (bound) electron to absorb lower-energy photons, as it's the electron whose orbital level changes. High-energy photons may be absorbed by the nuclear particles. But as to the actual question -- There's no way that two electrons could drop orbital levels and emit a single photon. There are (low probability) ways that the two emitted photons could interact in a nonlinear material via Stokes methods to produce a single final photon. – Carl Witthoft Jan 24 '15 at 13:46
  • @CarlWitthoft : I didn't say the nucleus absorbs the photon. But please see what I know. Indeed, the kinetic energy of the electron increases, but recall that we work with relative velocity and in the center-of-mass frame. Also the potential energy of the electron increases, as it orbits on a wider shell than before. This one energy is stored in the electron-nucleus field. (There was such a question in this site.) Let me put it otherwise: the photon that can be absorbed/emitted by the atom is in a range of much bigger $\lambda$ than the atom dimension. Such a photon sees all the atom. – Sofia Jan 24 '15 at 14:13
  • @CarlWitthoft : but let me know if I didn't convince you. – Sofia Jan 24 '15 at 14:18
  • @Sofia I only meant that we associate the potential energy with the bound electron rather than with the atom as a whole. – Carl Witthoft Jan 24 '15 at 17:21
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    @glance - For understanding the first part of my question you can read “Excitation of two atoms by a single electron” in Phys.Lett. 26A, (1968) 612. As for the second, the energy equation 2eV = hν of Josephson transitions affirms explicitly an emission in common of one photon by two distinct electrons. – Sava Jan 26 '15 at 07:28
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    @Sofia - The lighter expression “An atom absorbs a photon” actually means ”An electron in atom absorbs a photon”. – Sava Jan 26 '15 at 07:30

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The energy equation 2eV = hν of Josephson transitions affirms explicitly such emissions in common of one photon by two electrons, because in these experiments eV measures the energy difference ΔE between two energy levels involved in an electronic transition, and hν is the energy of the only photon emitted in common by two electrons after passing together from the higher energy level to that of smaller energy.

The Josephson transitions are the only electronic transitions deemed to be performed by pairs of electrons, and not by single electrons, as in all the other known transitions. Why? Certainly because these transitions have also been the only wherein someone succeeded in measuring directly both the energy variation ΔE of the involved electrons and the energy hν of monochromatic photons resulting from them. And the surprise was huge: experimental data ν and ΔE proved to have a proportionality factor h = ΔE/ν twice smaller than the action constant always used in theoretical physics!

In the face of such a challenge, instead of supplementary researches for verifying experimentally this value, it has been preferred simply to double the energy difference ΔE = eV in the energy equation of Josephson transition, by replacing the single electrons with pairs of electrons as performers of these transitions. An invention very simple and effective, because thus the known value of the action constant was saved, but a very disturbing doubt remains yet: can a pair of distinct electrons emit in common a single photon?

In my opinion, such an emission in common of one photon by two electrons is as nonsensical as an emission in common of one egg by two hens. Still my logic is classical. Maybe a virtual pair of quantum hens can indeed emit in common one egg twice larger than the usual eggs emitted individually by classical hens, exactly how a virtual pair of quantum electrons can emit in common one photon with energy twice higher than the energy of usual photons emitted individually by electrons under the same conditions. Maybe, I do not know the quantum logic.

For understanding the context in which this very questionable episode in history of physics appeared, you can also see my post “Emission and absorption of photons by electrons”.

Sava
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  • "can a pair of distinct electrons emit in common a single photon?" electrons within a potential well cannot be "distinct", it is a single quantum mechanical solution giving the probability of observing one photon emitted while two electrons change energy levels. If the probability is not zero, it can happen. – anna v Jan 27 '15 at 09:21