# Compton Scattering Notion

I have been reading about Compton Scattering and got confused about exact technicalities. So forgive me if I ask multiple questions, but all related to each other. This is due to the fact that you don't have to think about how to answer.

From Wikipedia,

Compton scattering is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. If it results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), it is called the Compton effect.

Q1: The above from wikipedia doesn't say anything about free electrons. There could be 3 cases: Which of these 3 are called compton scatter ? all of them ?

• an incident light that hits the electron that was already free(whether electron was at rest or already moving) and will speed up more.
• an incident light that hits electron that is bound to atom and it will cause electron excitement
• an incident light that hits electron that is bound to atom and it will cause electron ejection.

Q2: I wonder why compton scattering exactly applies to x-ray. I understand the experiment was done with x-ray, but if all 3 above in Q1 is called Compton, then it's a logic question to ask why visible light hitting electron is not called Compton.

• IIRC, it is provable that if the electron is free, then there would be no scattering of some certain types, because of needing to satisfy some conservation laws. The type of scattering that free electrons can do is just less varied than electrons near other stuff. May 3 at 2:18
• It might be a good idea if you could look at my other question that asks this: physics.stackexchange.com/questions/762337/…
– Matt
May 3 at 2:25
• Thank you in advance 🙏
– Matt
May 3 at 2:25

The terminology is a bit murky. We call the interaction of photons with free electrons "Thomson" scattering if the electron recoil is small enough to be neglected. This is true for visible light scattered by free electrons.

The interaction of photons with free electrons is considered "Compton" scattering if the electron recoil takes a significant amount of energy away from the photon. Additionally, we call it Compton scattering if the electron is bound before the interaction and unbound after, if the binding energy is small compared to the photon energy.

Compton scattering requires sufficient photon momentum to produce a significant electron recoil. That requires x-rays or gamma rays.

The probability of a photon interacting with an atom is parameterized as a "cross section". Different interaction processes have different probabilities. Which process occurs is random. Here, for carbon, $$\sigma_\tau$$ is the photoelectric cross section, while $$\sigma_{incoh}$$ is the Compton cross section. You can see that at energies below ~30 keV, the photoelectric process is more probable, while at higher energies Compton scattering is more probable. • Thanks for the answer. If binding energy of electron is 10eV, and photon hitting it is 12eV, it will eject the electron and have energy of 2eV. Don't we call this Compton Effect, if not, what is this called ?
– Matt
May 2 at 20:49
• @Matt It's a rare process. For photons below x-ray energies, interaction with a bound electron usually absorbs the photon. If it has enough energy to unbind the electron, we call the process the photoelectric effect. But yes, when the photon isn't absorbed we call it the Compton effect, although if the binding energy is significant the cross section and geometry are affected. Look up "Compton defect", and prepare for a journey down a deep rabbit hole... May 2 at 21:10
• This is super confusing. We call photoelectric effect when electron is ejected and the whole photon's energy is transferred to electron(no reflection of new photon). When you said that: "If it has enough energy to unbind the electron, we call the process the photoelectric effect.", Well, if that happened, it could happen that photon is reflected, hence it's not photoelectric effect anymore.
– Matt
May 2 at 21:15
• @Matt Yes, in the case where the photon is "reflected" in your terminology, we call it the Compton effect. This is rare for photons of energies lower than x-rays. May 2 at 21:34
• If x-ray is incident, which for sure causes electron ejection, what determines whether it's gonna be compton or photoelectric ?
– Matt
May 2 at 22:17