Suppose a slow-moving electron and a slow-moving proton are injected into a chamber, such that the two approach each other and are likely to combine to form an atom of hydrogen. How would one calculate the probable sequence of events, including likely emission of photon(s) over time? Will the resulting atom end up in ground state in a predictable sequence?

Note added later: I asked this question under the supposition that it was rather elementary. I was imagining a cold, dark box, sort of like an anechoic chamber, in which a photon might be emitted and never be heard from again, or better yet, a box surrounded by detectors which might record what was emitted and when.

I am still hoping there might be some such simplified approach. But I'm beginning to suspect I might be asking something much harder than I thought. Any comments will be appreciated.

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    $\begingroup$ This paper, “The Hydrogen Recombination Spectrum”, should be useful: adsabs.harvard.edu/full/1958MNRAS.118..477B $\endgroup$ – G. Smith Jun 22 '19 at 20:26
  • $\begingroup$ Thank you. I was hoping for a simpler approach, not involving radiation statistics. $\endgroup$ – Ralph Dratman Jun 23 '19 at 1:04

There are two basic types of recombination (of electrons with protons) into hydrogen atoms:

  1. ternary (three particles), this involves another electron, there is a transfer of energy of the order of the mean kinetic energy from one electron to the other

  2. radiative, emission of a photon, to conserve momentum (when the hydrogen atom relaxes to ground state), it has two types, SRR (spontaneous photo recombination), and TSRR (two step radiative recombination)

The radiative recombination (RR), the binding of a free electron with a proton(deuteron) accompanied by emission of radiation, plays an important role in astrophysicaland fusion plasmas. The RR is one of the most fundamental processes in atomic physicsand is connected to photo-ionization by the principle of detailed balance. Recombinationof electron to proton with emission of radiation can also take place in the presence of a third particle (electron or photon). The study of RR of electron with proton in the sponta-neous radiative recombination (SRR) channel, in absence of a third particle, dates back to1923 by Kramers [1] within a semiclassical approach.

Please see here:



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  • $\begingroup$ Just saw this so sorry for the delay. Much appreciated. $\endgroup$ – Ralph Dratman Jul 7 '19 at 1:44

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