On Thursday, 20 August 2015 09:31:35 AM Ethan Merritt wrote:
> On Thursday, 20 August 2015 09:36:55 AM Edwin Pozharski wrote:
> > typo indeed. The point, of course, stands - with older sources there are
> > *no* photons inside the crystal for over 99% of the time. (Notice that
> > diffraction pattern is still present, Bragg's law satisfied, etc)) X-ray
> > diffraction is, for all intents and purposes, a single photon experiment.
> > Even with the brightest and most coherent sources, when you could have
> > multiple photons within a large crystal, these are still separated in space
> > by a distance that is at least 100x the coherence length.
>
> [just a tangential comment]
> Consider an XFEL source: picosecond pulse, micron crystal.
Sorry sorry.
** femtosecond ** pulse (not picosecond)
> The spatial length of the pulse is less than the size of the crystal.
> I do not know how to calculate the exact coherence length, but my
> understanding of the SASE XFEL process is that it should be about
> the same as the pulse length, since that is how the pulse forms.
>
> Ethan
>
>
>
> > Thus, X-ray
> > photons do not interact with each other (and even if they would, it's still
> > does not make them a wave, just good ole photons that due to their high
> > spatial density would have detectable probability to engage in multi-photon
> > events).
> >
> > On Wed, Aug 19, 2015 at 5:13 PM, Keller, Jacob <[log in to unmask]>
> > wrote:
> >
> > > >Also, if your X-ray source is not exactly the brightest synchrotron, you
> > > are probably looking at ~10^9 photons/sec at best (I am estimating here
> > > that it would take at least 15-20 minutes of data collection using early
> > > 2000s "RAxisIV" in-house system to get diffraction image of intensity
> > > similar to 0.5s exposure at 12-2). That is one photon every nanosecond.
> > > Let's continue to ignore the fact that most photons just fly through. A
> > > photon zips through a 1mm crystal in about 3fs. Think about this - at a
> > > moderate intensity home source (and I can go to sealed tubes), the process
> > > of crystal illumination by X-rays is more like single photons flying
> > > through with about 300x long pauses between events. To scale this, imagine
> > > that a single photon spends a whole second inside a crystal, probing it's
> > > electron density. You would then have to wait five minutes for the next
> > > photon to arrive.
> > >
> > > I was re-thinking through this, and I think one of these numbers is wrong,
> > > viz, “A photon zips through a 1mm crystal in about 3fs.” The speed of
> > > light is 3x10^8 m/s, so this leads to ~3.3 ps for a 1 mm path, and not 3
> > > fs, a difference of ~10^6. Maybe it was just a typo? Anyway, it may not
> > > make a huge difference, since this would still make for an average of ~1
> > > photon in the crystal at a time, assuming a high flux of 10^12 photons per
> > > second. But of course there would be some Poisson statistics involved, and
> > > there would be several photons a significant part of the time.
> > >
> > > Also, I wonder about relativistic effects: in the famous train-in-tunnel
> > > thought experiment, a large train can fit in a short tunnel if it’s going
> > > close to the speed of light. Is this applicable here, such that many
> > > photons are in some sense in the crystal at once? Or maybe this is a red
> > > herring.
> > >
> > > But, to change topics a bit: part of the reason I am wondering about this
> > > is anomalous scattering. Since the resonance energy of an atom is a fixed
> > > amount, how can one photon provide that energy simultaneously to the
> > > requisite number (at least thousands, I would think) of resonant
> > > scatterers? Something’s very funny here.
> > >
> > > Or, come to think of it, perhaps resonant scattering is no worse than
> > > normal scattering: if the energy is divided up between the all the
> > > normally-scattering electrons, you even have a problem with the one-photon
> > > picture, since the emerging radiation is still of the same energy. You want
> > > to have everything being scattered with a certain energy, but you also want
> > > all the scatterers to scatter. The concept of “energy” seems to get
> > > strange. Does one then need two terms, in which “energy” is just a
> > > characteristic of radiation, like a color, and then there is some other
> > > attribute like “probabilistic intensity,” which describes how much “photon”
> > > is there?
> > >
> > > It is striking to me how much depth these everyday occurrences really have
> > > when one starts wondering about them.
> > >
> > > Jacob
> > >
> > >
> > >
>
>
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