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3

Eq. 6.68 as you quote it seems wrong. Here's how to argue better that the delta functions should "vanish": The Born approximation says that the scattering amplitude for a momentum $\vec p$ into a momentum $\vec p'$ is $$A_\text{QM}(p,p') = (2\pi)\delta(E_p - E_{p'})(-\mathrm{i})\langle \vec p\vert V\vert \vec p'\rangle,$$ and the corresponding ...

2

The microscopic scattering cross section- and the differential microscopic scattering cross section- applies to one scattering event for one target atom/nucleus. The microscopic differential cross section is that fraction of the microscopic scattering cross section for scattering into a solid angle. The cross section for any reaction (fission, scattering, ...

2

Here is the Feynman diagram for Compton scattering: A Feynman diagram is the pictorial representation of of the integral needed to calculate an interaction crossection, and depending on how you read the axis it describes the corresponding interaction. If the x axis is taken as time, it describes the scattering of an electron on a photon, and a new photon ...

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This is a partial answer because I am not going to discuss the many different ways it is possible to change photons' frequency. I want to emphasize an issue related to the way the question has been formulated. I think it may be useful to appreciate the meaning of changing the frequency of a photon, whatever method is used. Photons are definitely neither like ...

1

tl;dr: In principle, yes at the amplitude level, but no at the rate level. In the Standard Model, no, not at all. I assume you are talking about something like "photon decay in vacuum" because you say "lone photon." So I won't consider photon conversion due to interactions with some other particle, for which there are more possibilities. ...

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The first one is for the amputated diagrams, which do not contain any external legs. The second one is the full matrix element plus the delta for the conservation of momentum. The delta for the conservation of momentum is not fundamental, since it can be added at any moment when evaluating cross sections. From my experience, i'd rather put the conservation ...

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