Formation of hydrogen atom by electron proton collision

Question

Suppose we have an electron $e$ and a proton $p$ colliding to form a hydrogen atom that is the reaction $e+p\rightarrow H + \gamma$ where $H$ is an hydrogen atom and $\gamma$ is some photon.

The scattering amplitude should be I think $A=\langle \gamma , \psi |S|e,p\rangle$

Here $\psi$ is a Hydrogen bound state.

Is there any book or paper that treat this problem?

Much (most?) of the literature on this topic is likely addressable through the search term "radiative recombination". — Emilio Pisanty, Dec 02 '20 at 14:48
@EmilioPisanty - as long as one avoids all the semiconductor LED and laser literature... — Jon Custer, Dec 02 '20 at 14:58

score 1 · Answer 1 · edited Dec 07 '20 at 15:08

As it has been already mentioned, radiative recombination is one possible keyword to look for, provided that one restricts one's search to atoms.

Another place to look is inelastic collisions chapters, possibly even in basic QM textbooks. E.g., Landau&Livshits have a chapter on inelastic scattering, but I am not sure, whether they discuss exactly this problem. They however do discuss intra-atomic transitions while electron is scattered from the atom.

Yet another option is X-ray absorption. In the context of semiconductors it is definitely discussed in the texts on many-body physics, but those focus mainly on the subsequent restructuring of the Fermi sea, known as the Andreson orthogonality catastrophe.

Formation of hydrogen atom by electron proton collision

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