perturbative Compton

[szabo137]

This PR adds one photon Compton scattering described in perturbative QED.

This includes the following variants

• diff. probability and cross section on momenta
• diff. probability and cross section on coordinates (electron restframe and spherical coordinates)

All implementations are done for arbitrary combinations of spins and polarizations.

Todos

• discuss where the spins/polarizations are stored: proc or phase space point (be aware of dispatch)
• add total cross section
• add unit test for total cross section
• add unit tests for phase space point input

[AntonReinhard]

What's the general state of this now?
Trying to rebase to dev seems to be a nightmare, but merging dev back into this branch should be pretty easy. Other than that, some things need to be adjusted now to the PhaseSpacePoints and ParticleStateful types I believe.

[szabo137]

What's the general state of this now? Trying to rebase to dev seems to be a nightmare, but merging dev back into this branch should be pretty easy. Other than that, some things need to be adjusted now to the PhaseSpacePoints and ParticleStateful types I believe.

I followed your advice and merged dev into this one. Now this should be up-to-date and ready for discussion. There are some open questions we could think about first (see the description box above).

[szabo137]

As we discussed offline, we want to merge this PR without connecting to the phase space points, and then we want to open a separate PR for the change of the diffCS interface to phase space points (see #57).

@AntonReinhard I added the total cross section, so there are no open todos. I think this is ready for final review.

[szabo137]

Certainly, there was a bug in _incident_flux which was only present in Julia versions below 1.10.

TL;DR:
In the tested versions (1.6 to 1.9), the function prod(::Vector{AFM}) consuming a vector of four-vectors returned Union{Float64,<:StaticArray}, which is clear since the compiler does not know anything about the number of elements passed to prod. However, since for Compton we know that length(in_ps)==2, we can just index into the vector and use the mul function.

Edit: now everything should be ready.
Edit2: The bug was actually caught by the @inferred macro, which we should use more often in the unit tests.

[AntonReinhard]

Looks good