exchemist
Valued Senior Member
The electron is bounded (localized in a region of space) over the two photons since it is placed in the middle. It is actually a standing wave setup with the electron entrapped within.
Alternatively the argument is as follow: The Compton Scattering process is known and experimentally verified, right. Then two mirrored Compton Scattering processes actually cancel the Scattering process (over the momentum conservation). At that moment appears the paradox (as I call it) where the electron seems to absorb both photons (there are no scattered photons therefore they are absorbed) leading to an increased electron Energy without to change its initial null kinetic Energy. Now under such circumstances (trapped in between of two photons) and in order to hold the Energy conservation, the electron is forced to reduce its total Energy. That is all!
No it isn't "entrapped". A bound state means the electron experiences a potential that confines it, i.e. the sum of its potential and kinetic energy is insufficient to enable it to escape into free space. The electron is not "trapped" at all, in your scenario. It is free. Semi-classically speaking, it can move laterally in response to the electric vector of the radiation coming at it from both sides, and thus oscillate in sympathy with the two photons. It may move laterally and give rise to Compton scattering of both photons. So I think you are incorrect to suppose that the two Compton scattering possibilities are cancelled out. Don't forget that in Compton scattering the angle of the photon must change if any energy is absorbed by the electron. That implies the electron acquires some momentum in a direction perpendicular to the direction of the incident photon.
And I feel sure you are quite incorrect to state that "there are no scattered photons therefore they are absorbed". In most cases, the photons will simply pass by and each will emerge unchanged at either side. So there are no scattered photons, but no absorption either.
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