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If an atom builds up from an ion capturing an electron which state of the atom is more probable as a first transition (immediate after capturing) - with higher energy (excited state) or lower (more close to nucleus - e.g. ground state or some higher than ground). What is the reason and is there a mechanism? Also is it possible by some conditions to prohibit higher levels (maybe a tuned appropriately cavity) and the recombination to take place only and directly on the ground state?

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I suppose you surely mean will it jump from the initial free state directly to a low-energy bound state or go there gradually through higher-energy states.

I would say if the electron initially have high angular momentum, and if the atom is isolated and can only de-excite by emitting photons, because usually only lower multipole emission of photons happens (as others are much slower), the atom can only go to the lowest-energy state compatible with the initial angular momentum, and then shed angular momentum and go to lower energies gradually by emitting series of photons.

So my views is, it depends on the initial angular momentum. It will quickly go to the lowest energy state with angular momentum one or two $\hbar$ away from the initially free state. Whether this state has a high or low energy depends on atom's energy-level structure as well as the initial angular momentum.

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  • $\begingroup$ as I recall from ALPHA [cern's anti hydrogen makers], atom formation is a 3 body process...a lone $e^+$ and $\bar p$ can't do it while conserving $E$, $p$, and $L$. $\endgroup$
    – JEB
    Jul 27, 2021 at 15:24
  • $\begingroup$ As far as understand you mean the following: in the ions own reference frame the e- is passing on a distance d and is captured on an Earths-like orbit whereas all its kinetic Energy converts to rotational and L=Nh. Then is releases photon and gets to lower orbit with L=(N-1)h. But then the energy levels would be equidistant (at least approximateIy) I wonder where do then the Energy levels come from with their composite structure? $\endgroup$
    – Mercury
    Jul 27, 2021 at 18:36
  • $\begingroup$ @JEB But wasn't it after the big bang just protons and electrons. How did they build H? I always thought from elementary physics that when one has two opposite charges they attract and build an atom whatever their p, E and L. $\endgroup$
    – Mercury
    Jul 27, 2021 at 18:37
  • $\begingroup$ @JEB Thank you for your information. I remember the point you mentioned. Nevertheless, I have in mind that the ion captures the electron by emitting a photon. So I think it is a three-body process. $\endgroup$
    – aystack
    Jul 28, 2021 at 10:01
  • $\begingroup$ @Mercury I wrote the answer having in mind a quantum mechanical point of view. And I would say to understand it fully one has to know the basics of quantum mechanics. Nevertheless, I will try to reply. 1, " captured on an Earths-like orbit whereas all its kinetic Energy converts to rotational", as JEB mentioned, without photon emitted, it is a two-body process and capture cannot happen. $\endgroup$
    – aystack
    Jul 28, 2021 at 10:18
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which state of the atom is more probable

It depends on the state of the electron and atom being far apart and their relative motion. The process of electron capturing should satisfy the following conditions:

  1. energy conservation: kinetic energy of electron + total energy of ion = total energy of atom after capturing.

  2. wave function overlap (electron and ion should be located in the close vicinity for capture to happen). The excited states of ion/atom are more spread in the space - they will overlap with incoming electron wave function first.

These two conditions make me believe that the atom will be in a highly exited state after capturing the electron. So, we should observe the relaxation process with emitting photons afterward.

I think such electron capturing can be seen as an inelastic scattering process in a way - the free-electron loses all its energy and seize to exist - electron and ion annihilate and an excited atom is created.

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An ion is built up by losing the outermost and least bound electron. If there is an electron in the vicinity afterwards, it is placed at this outermost position.

Only if an electron with high kinetic energy hits the ion is it possible for electrons further inwards to be displaced.

In both cases, photons are emitted.

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  • $\begingroup$ I don't think 'outermost position' makes any sense. $\endgroup$
    – Jun Seo-He
    Jul 28, 2021 at 16:37
  • $\begingroup$ This is the answer to a different question than what’s asked here. $\endgroup$
    – rob
    Jul 28, 2021 at 17:15

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