Suppose a photon with wavevector k is being elastically scattered from, say, an atom into a state with different wavevector q, does it make sense to ponder the (average) duration of such an event?
I would guess the answer is yes, if there is a real intermediate excited state of the atom involved (and the lifetime of that state shall play a dominant role). I don't know what to guess in case of a virtual intermediate excited state.
Well, I cannot answer 'yes' or 'no'. I haven't seen such investigations yet. But after all, such phenomenon is a bit similar to radioactive decay. And we are (were?) very interested in lifetime of various radioactive isotopes. Nowadays, in nanotechnology era the duration of light scattering event may appear quite important. We can also suspect that this effect may have very different lifetime in gases or solids when compared to cosmic conditions.
Dear Kai,
Perhaps a Nonlinear Raman Effect could allow to "control" the decay lifetime with enough accuracy.
https://www.nature.com/articles/srep01842
Isn't this what is normally described in terms of linewidth of the peak in resonant scattering? For a very-very narrow peak this may be more naturally described directly as a retention time or scattering time. But then the peak may be so narrow that it can't be found, so the whole effect becomes impossible as an observable phenomenon.
With inelastic scatting however... like when a cosmic ray excites a carbon nucleus, which after some internal conversions settles down in the very long lived ground state of a C14 nucleus, which after some hundred years decays back to the original nucleus. We would not call this a scattering event, though; there must be some blurry transition region beyond which scattering becomes a misleading description.
It has made sense to me to map RIs of particulate mixtures, which boils down to measuring the speed of light through each encountered particle, against ordinates and abscissas related to Planck's and de Broglie's Laws. Average effects are calculated for each point studied on the mapped surface. If one considers only one incident wavefront, the net differences among resulting multiple wavefronts relates to durations of photon travel time through particles at each particular point of the field studied.
I hope that pertains to your question. :-)
-Steve-
Dear Kai,
as far as I can understand, your question is related to the absorption + emission (scattering) times in a reference frame at rest with the atom.
We can reasonably assume that the absorption and emission times are the same in an elastic scattering event.
The problem can be reduced to understand what can be the absorption time of a photon by an atom.
It is reasonable to find some upper bounds for such time...
An upper bound should be trivially related to the time light takes to cross the diameter of the atom, it cannot be more than that, since otherwise the photon would cross it.... the train would leave... it may not be in general a fix time.
The upper bound for such time should be some angstroms divided by the speed of light. For Hydrogen for example it should be less than 10^-10 m/(3*10-8 m/s)
something like 3,3*10-18 s.
The scattering time should be not higher than 7*10-18 s in the case of Hydrogen.
In case of Nuclear gamma scattering the time should be in the order of magnitude of 10-23 s.
The lower bound is trivally the Planck time...
Stefano, I don't actually buy that. An absorption time can be considered in case the absorption resonance is being met. I would actually spontaneously agree that absorption and emission time should be the same. However, this would then imply an analogous lifetime of the excited state. With such short a life time as you propose (7*10-18 s) there should be no atomic line with a linewidth below some 100eV. This is inacceptable to me!
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