collisionconservation-lawsmomentumquantum-electrodynamicsscattering
With Compton scattering the total momentum and the total energy of the photon electron system is conserved, so it has to be ELASTIC Collision/Scattering.
But an argument is that just because the kinetic energy of the incoming photon is different than the outgoing photon, it is INELASTIC Collision/Scattering.
However, I thought we had to look at the system, which is the photon and electron interaction; not just the scattered photon itself.
So, what is the real issue here?
What is the difference that leads to conservation of kinetic energy in elastic collision ?
The difference is only in the properties of the material of a body. If it is elastic (happy ball) it can deform itself (thus absorbing KE) and then recover the original shape, giving back roughly the same amount of KE, which is considered as temporarily stored in the lattices: this question can be of help to you if you want a deeper insight.
You saw this image here: If a body is not elastic (sad ball) the KE will deform the body and this change is irreversible, the KE will be transformed into heat, sound etc. and will not be available anymore as mechanical energy. In this video you can see the enormous difference between a sad and a happy ball of same mass and momentum. If the concept of impulse is not clearly explained there this answer can be of great help
Why is mechanical energy converted as total energy is conserved in inelastic collision?
Kinetic energy is transformed into an exactly equal quantity of other forms of energy in inelastic collisions, therefore the total energy of the system does not change: KE is not conserved whereas momentum is, but energy in general is conserved anyway
Raman scattering is inelastic scattering from molecules. The photon interacts with the molecule and changes the molecules vibrational, rotational or electron energy.
Rayleigh scattering is in the main elastic scattering from small particles whose size is less than that of the wavelength of the photon. The scattering can occur of atoms or molecules and for molecules the scattering can be inelastic with a change of rotational energy of the molecule.
Compton scattering is inelastic scattering of a photon from a free charged particle. If the charged particle is a bound electron then the energy of the photon must be much greater than the binding energy of the electron.
Side note: Rayleigh scattering is a particular case of Mie scattering. This theory explains in particular the white colour of objects which are made of particles of size greater than the typical wavelength : milk, clouds, chemical powders...
To add to the answer there is Thomson (no "p") scattering which is the elastic scattering of electromagnetic radiation by a free charged particle, as explained by classical electromagnetism.
It is just the low-energy limit of Compton scattering when the particle kinetic energy and photon frequency do not change as a result of the scattering.
This limit is valid as long as the photon energy is much smaller than the mass energy of the particle.
Best Answer
The definition of inelasticity differs between dynamics and particle physics.
In the former, inelasticity refers to the loss of kinetic energy in the system as a whole, as some is lost (e.g. heat).
In the latter, it refers explicitly to the loss of kinetic energy of the incident particle. In the case of Compton scattering, that means the loss of photon energy.