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Is it possible to generate more photons just by collision?

Initially I thought it is possible in an atom because electron would absorb energy and get excited and then come to ground state in more than one step so more than one photon gets released. But will more photon be generated if the particle was a free electron?

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You are misreading the statement,

The photon may be absorbed

means that the particle is a composite one, so that the photon may raise the atom, for example, to a higher energy level, the photon absorbed completely.

or a new photon may be created

Means if the scattering is not elastic, part of the energy of the photon is transferred to the particle and a lower energy (new) photon leaves, as in Compton scattering , look at diagram b here.

It is true that photon number is not conserved, but each photon particle-vertex depresses the crossection by a factor of (1/137) at least, so extra photons are not very probable. If the electron acquires a lot of energy in the compton scatter it may interact with a field of an atom and give off a second photon, but that is not what the statement is about.

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