Help explaining the ion-electron recombination process

[papernuke]

I don't know the process in which a free electron finds its way back down to the ground state of a hydrogen ion and thus forming a neutral hydrogen atom.

I have tried my hand at Googling the topic, but I can't seem to find any detailed websites about the electron-ion recombination for hydrogen H ions (a proton).

Could someone please help explain the process or direct to a link?

Thanks!

 

[K^2]

A free electron can still be decomposed into spherical harmonics around an ion. So it's the same process as electron simply going from a higher energy level to a lower one. The difference is that initial state might not be an eigen state of your system, so you would probably end up with a superposition of frequencies being emitted. But since all of these will be nearly degenerate, it won't really matter.

 

[papernuke]

So in terms of the energy levels, is it like simply having the new electron start at n=infinity or some other high n and undergoes transitions down?

The difference is that initial state might not be an eigen state of your system, so you would probably end up with a superposition of frequencies being emitted. But since all of these will be nearly degenerate, it won't really matter.

And could you please explain this bit again in simpler terms?

 

[Drakkith]

I don't think a transition has to be from one energy level to the next one up or down. It can be almost any jump, especially when moving down energy levels. I think at least.

 

[K^2]

I don't think a transition has to be from one energy level to the next one up or down. It can be almost any jump, especially when moving down energy levels. I think at least.

So long as conserved quantities are conserved, yes. So angular momentum, for example, has to change by one per emitted photon.

And could you please explain this bit again in simpler terms?

Only certain states can be written as specific l,m,n combination. An arbitrary state has to be written as some linear combination of these. Energy an arbitrary state needs to lose to go to ground state also isn't going to be exactly equal to any of the available transitions. But that's kind of the point of the quantum mechanics. You can emit a photon that's in superposition of several different energy states. And that's what will have to happen as free electron gets captured.