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The comments by KF Gauss are on the right track: non-relativistic quantum electrodynamics (NRQED) is a good foundation. The question is then how to recover the "effective potential" description of X-ray diffraction from NRQED. This isn't my specialty, but I reviewed the NRQED derivation of elastic X-ray scattering from a crystal, using the references listed ...

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When a photon interacts with an atom, three things can happen: elastic scattering, the photon keeps its energy and changes angle (mirror reflection) https://en.wikipedia.org/wiki/Elastic_scattering inelastic scattering, the photon keeps part of its energy and changes angle (photon transferring vibrational and rotational energies to the molecules, heat up ...

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The problem with fixed-target experiments it that you have to make the target, then install the target, then irradiate the target with your beam. If your target is short-lived, the timescale for each of these steps becomes more challenging. For example, in positron-emission tomography, the positron source is usually fluorine-18, which has a two-hour half-...

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Angular momentum is $\mathbf{L} = \mathbf{r} \times \mathbf{p}$. Thus by definition, the impact parameter is a ratio of the magnitudes of angular momentum to linear momentum. $$b = \frac{L}{p}$$ From the energy-momentum 4-vector (assuming units with $c = 1$), $$E^2 - p^2= m^2$$ $$p = \sqrt{E^2-m^2}$$ b = \frac{L}{\sqrt{E^2-m^2}}=\frac{L/m}{\sqrt{(E/m)^2-1}}...

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In the beams we have in the laboratory, the particles do not superpose or interact with each other, due to the large space time distances for the individual particles in the beam. Within our experimental accuracies it is as if each electron is all alone in the universe when interacting with a positron. Whether polarized or not each incoming particle can be ...

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