Suppose a region of empty space, to which we add one proton and one electron, initially separated by a distance on the order of centimeters, and as close to "at rest" in the center-of-mass frame as we can practically achieve.
They will of course attract each other and combine into a hydrogen atom, emitting at least one photon in the process. I'd like to understand this process in detail. Specifically: for an initial separation this large, it seems likely that the system will not emit just one photon and go directly to the 1H ground state, because that photon would be very energetic. Instead there would be some number of bremsstrahlung interactions, followed by atomic orbital transitions, before reaching the ground state.
- How does one model this quantitatively?
- What would the typical number of emitted photons be, and what would their wavelengths be?
- How small can you make the initial separation before the most probable outcome is just one emitted photon?
- How does one draw the line between "bremsstrahlung" and "atomic orbital transition" in a system like this?
- What is the (ballpark) probability of something else happening, such as a weak interaction producing a neutron? (That's the only possible "something else" I know of. Are there others?)