Compton scattering angle question

[Borg]

I've been reading some of my old physics books and I'm currently reading about Compton scattering. It got me to thinking - is there is a minimum Compton scattering angle? Is there a point where it becomes highly unlikely (or impossible) for a photon to be Compton scattered?

 

[Astronuc]

The answer depends on the photon energy and electron. For low energy photons, they are likely to be completely absorbed. As energy increases, photons are more likely to survive, and subject to Compton scattering. There is a continuous spectrum of energies in Compton scattering and there is a maximum change in energy. The minimum scattering angle is close to zero and the maximum angle would be 180 deg, but there is perhaps a higher probability that the scattering will be in between. Ostenstibly the result depends on the geometry of the interaction, and energies/momenta of the electron and photon.

There is also inverse Compton scattering whereby a higher energy photon is produced.
http://www.cv.nrao.edu/course/astr534/InverseCompton.html

http://www-ppl.s.chiba-u.jp/lecture/radiation/node5.html

 

[phyzguy]

Astronuc: I don't understand your answer. Compton scattering is a process between photons and free electrons. I don't think the photon can be absorbed, because then energy and momentum cannot both be conserved. Am I missing something?

 

[Borg]

Astronuc: I don't understand your answer. Compton scattering is a process between photons and free electrons. I don't think the photon can be absorbed, because then energy and momentum cannot both be conserved. Am I missing something?

From what I've been reading, a free electron can refer to an electron that has a small enough binding energy with respect to the photon energy such that the binding energy can be ignored and the electron can be considered 'free' (assuming, of course, that I'm remembering everything correctly ).

 

[Astronuc]

Astronuc: I don't understand your answer. Compton scattering is a process between photons and free electrons. I don't think the photon can be absorbed, because then energy and momentum cannot both be conserved. Am I missing something?

I was referring generally to photon-electron interactions. Also, Compton scattering can occur with atomic electrons, which are bound by energies on the order of ev (e.g. valence electrons) or keV for first orbital electrons of heavier elements.

Those energies compare to X-ray photons with energies (originating from electrons falling into the K or L shells) in the keV range or gamma rays of keV or MeV energy.

 

[Borg]

The answer depends on the photon energy and electron. For low energy photons, they are likely to be completely absorbed. As energy increases, photons are more likely to survive, and subject to Compton scattering. There is a continuous spectrum of energies in Compton scattering and there is a maximum change in energy. The minimum scattering angle is close to zero and the maximum angle would be 180 deg, but there is perhaps a higher probability that the scattering will be in between. Ostenstibly the result depends on the geometry of the interaction, and energies/momenta of the electron and photon.

There is also inverse Compton scattering whereby a higher energy photon is produced.
http://www.cv.nrao.edu/course/astr534/InverseCompton.html

http://www-ppl.s.chiba-u.jp/lecture/radiation/node5.html

I guess that I should make some assumptions about my question. Let's say that I have a truly free electron that isn't bound and a photon interacts with it at an extremely small grazing angle such that the electron gets the least amount of energy possible.

Could the angle be so small that the wavelength shift would approach zero and the electron deflected so slightly that its velocity would be on the order of a walking speed?

 

[Astronuc]

I guess that I should make some assumptions about my question. Let's say that I have a truly free electron that isn't bound and a photon interacts with it at an extremely small grazing angle such that the electron gets the least amount of energy possible.

Could the angle be so small that the wavelength shift would approach zero and the electron deflected so slightly that its velocity would be on the order of a walking speed?

If that were the case, then I don't think it would be measurable. If a keV or MeV photon changed energy by 1 eV, that would be challenge to measure. It might be considered non-interacting.

Free electrons are probably moving at well beyond 'walking' speed if walking refers to velocities of a few m/s.

At thermal energies, ~0.0235 eV, neutrons move at about 2200 m/s. Electrons being about 1/1839 of the mass of a neutron, a free electron would have a higher speed.

Unless it has a high speed, as in a plasma, an electron would likely find a convenient + nucleus and bind with it.

 

[Borg]

Thank you, Astronuc.