On 2003-01-29 21:25, Tim Thompson wrote:
JK: Where did you get the idea that photons with less energy than the rest energy of an electron don't scatter from electrons?
From Classical Electrodynamics
, J.D. Jackson, John Wiley & Sons, 3rd edition, 1999. See section 14.8, pp.694-697.
"The classical Thomson formula is valid only at low frequencies where the momentum of the incident photon can be ignored. When the photon's momentum hbar*omega/c
becomes comparable to or larger than mc
, modifications occur. These can be called quantum mechanical effects, since the concept of photons as massless particles with momentum and energy is certainly quantum mechanical (pace
, Newton!), but granting that, most of the modifications are purely kinematical. The most important change is the one observed experimentally by Compton. The energy or momentum of the scattered photon is les than the incident energy because the charged particle recoils during the collision." (pp. 695-696).
The same discussion occurs in section 14.7 of the 2nd edition, which I have from my student days and is probably more common on bookshelves.
From Radiative Processes in Astrophysics
, G.B. Rybicki & A.P. Lightman, John Wiley & sons, 1979. See chapter 7, p.195, "Compton Scattering".
"For low photon energies, h*nu very much less than mc^2
, the scattering of radiation from free charges reduces to the classical Thomson scattering, discussed in chapter 4." The authors go on to develop the theory of Compton scattering & inverse Compton scattering in great detail.
JK: The Klein-Nishina formula gives the cross section and it reduces to the Thomson cross section for a free electron.
Correct. However, in the Klein-Nishina formula, the cross section is energy dependent. Compton scattering becomes less efficient at higher energies (see Rybicki & Lightman, p. 197). This in turn means that the optical depth for Compton scattering is also energy dependent. That's why the Compton effect cannot produce a wavelength-independent redshift, because the scattering optical depth is wavelength (energy) dependent.
It may not be exactly correct to say that Compton scattering does not occur at all for low energy photons, but it is correct to say that the scattering optical depth will drop so close to zero that Compton scattering ceases to be a physically significant process at such low photon energies. Compton himself discovered the effect with X-rays, where photon energies are high enough to make the process work.
<font size=-1>[ This Message was edited by: Tim Thompson on 2003-01-29 21:26 ]</font>