What is the difference between coherent and elastic scattering? Maybe the elastic scattering implies that there is no loss of energy, whereas the coherent scattering implies that the wavelength of a beam is the same before and after the scattering?

# [Physics] Difference between coherent scattering and elastic scattering

coherencescattering

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Rayleigh scattering is scattering from polarizable entities. The incident light induces a dipole moment, which re-radiates. Thomson scattering is scattering from free unbound charged "unpolarizable" particles.

The cross section for Rayleigh scattering decreases with the fourth power of wavelength. That for Thomson scattering is independent of wavelength.

Comparing their relative cross sections is tricky, because Rayleigh scattering depends on the size of the particle, the wavelength of light, and the polarizability of the particle, all of which can vary significantly. Thomson scattering has none of that.

The Wikipedia pages you cite have a few examples. Air in visible light has a Rayleigh cross section on the order of $10^{-31}\, \mathrm{m}^2$, and the Thomson cross section for an electron is on the order of $10^{-28}\, \mathrm{m}^2$

I agree with @Floris that the statement doesn't make sense at face value, but since I know what he is trying to say, I might be able to translate.

No signal has a single frequency. There is always a very small spread in a signal's frequency content. (Pure single frequency implies a signal that started in the infinite past and will continue into the infinite future.) But a nearly-single-frequency wave will be indistiguishable from a true-single-frequency wave if you look at it for a finite time interval.

So take two waves, and look at them during the same time interval. They both will look like waves with some frequency $f$, with some phase shift $\phi$ between them.

Now wait a while and look at the same two waves again. Again, they both will look like waves of frequency $f$. And they will have a phase shift between them, call it $\phi_\mathrm{new}$.

If you wait a short enough time between measurements, the two phase values will be the same. If you wait long enough, they will have been seen to have drifted apart.

Over time, $\phi_\mathrm{new}$ drifts away from $\phi$ because of those tiny fluctuations in the frequency. If $\phi_\mathrm{new} = \phi$ we could say that there is a constant phase shift; if not, then we can say that the phase shift is not constant.

Optical detectors average intensity over a long time, often on the order of seconds. If the phase shift is not constant during that interval (an incandescent source for example), interference patters will be washed out, and not visible. The light is *incoherent* over that interval. If the phase shift is constant over the (e.g. a laser), interference patterns are visible. The light is said to be *coherent* over the interval.

## Best Answer

In the literature, the two terms are often mixed up and used differently. In my answer, I will use the most distinct and most common interpretation of the two.

In simple terms,

elastic scatteringis about. Specifically, "the kinetic energy of the scattering particle is conserved in the center-of-mass frame" (see wikipedia). Inelastic scattering is then a process where the scattering particle loses energy (see wikipedia).energyCoherentvs.incoherentscattering is not about energy, it is about theorphaseof a the wave or scattering particle. There does not seem to be a wikipedia article on coherent scattering, but there is one for incoherent scattering. Coherent scattering is then the case where the scattered particle or wave has a fixed phase relation relative to the initial wave, such that you can observe interference between the two. This coherence can be destroyed by fluctutations of the scattering medium or by quantum effects such as inversion of level systems.fluctuationsImportantly, all combinations of the two categories are allowed. That is coherent elastic scattering, incoherent elastic scattering, coherent inelastic scattering and incoherent inelastic scattering are all different physical processes.

In mathematical terms, the processes can be categorized by properties of the difference between the initial and final state of the scattering particle in the scattering process $\psi_i \rightarrow \psi_f$. For elastic scattering, $\psi_i$ and $\psi_f$ have the same energy, for inelastic scattering they do not. To investigate incoherent scattering, one usually leaves the framework of wavefunctions and introduces density matrices or statistical ensembles. A common example of coherent and incoherent scattering is the famous Mollow triplet in resonance fluorescence, where both processes occur simultaneously.