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Can someone walk me through in detail what happens when an atom is ionized by colliding with an electron?

I would prefer a solid example so I can understand it more concretely.

What I think:

  • The electron collides with the atom giving it energy, but then goes away after that.

  • This energy excites an electron inside the atom, which receives enough energy to leave the atom.

  • The atom is ionized.

However, I also thought of another way:

  • The electron collides with the atom and gets bound up in the atom.

  • The atom is now ionized (negative ion, since extra electron)

Are any of these descriptions correct?

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    $\begingroup$ Short answer: both processes are possible (although your explanations are not reflecting the actual processes well, which can only be explained by quantum mechanics). Which is taking place depends on the energy of the incident electron, the energy spectrum of the atom and the (possibly) resulting ions and whether a third partner is available for taking momentum. $\endgroup$ – Sebastian Riese May 10 '15 at 23:20
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    $\begingroup$ The problem with ionization and other scattering processes is, that there is no obvious classical description of what is happening. The evolution of the state during the scattering process will require the summation of many different multi-body diagrams in a quantum field theoretical description, the meaning of which (especially in their linear superposition) does not correspond to a naive physical interpretation. The situation is a little better in quantum-chemistry, where the movement of the nuclei is essentially classical, but in e-e scattering there is no such slow timescale. $\endgroup$ – CuriousOne May 10 '15 at 23:32
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    $\begingroup$ To shorted @CuriousOne's nice comment: you are now asking questions for which a "little billiard balls" model of the atoms is completely useless. $\endgroup$ – dmckee May 11 '15 at 0:27
  • $\begingroup$ Hi. As the comments above state, as a first approximation, you are correct. But I think it' s a little difficult for someone to post here a QFT answer, for something that can be studied when you get involved with it. $\endgroup$ – Constantine Black May 18 '16 at 19:05
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    $\begingroup$ Only processes resembling the first scenario are called ionization. The second is called electron capture. $\endgroup$ – Arnold Neumaier May 18 '16 at 20:18
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To combine some of the comments that have already been stated, plus some extra remarks, into something more formal:

  • The second process described in the OP is not usually called ionization (even though the end result is an ion), but rather electron capture.

  • In general, though, this cannot happen exactly as stated for an isolated atom $A$ capturing a free electron to form its negative ion $A^-$, because the state $A+e^-$ with a free electron has more energy than the bound state $A^-$. This energy must then be emitted in some way, which can be the emission of a photon, excitation of internal degrees of freedom (specifically, the nuclear motion in a molecule), or delivering a kick to some third body in the neighbourhood.

  • Ionization by electron impact usually denotes processes of the type $$ A + e^-\to A^+ + 2e^-,$$ where the initial electron has enough energy to 'tear' out one of the electrons of $A$ to create a positive ion $A^+$ plus a second free electron.

  • However, the sequential picture described in the OP (the first electron deposits energy and goes away, and only afterwards is the deposited energy used to eject the second electron) is in general unlikely to be a good model compared to a single-step model where the second electron is ionized immediately during the collision.

    Telling apart these two processes experimentally, on the other hand, can be rather tricky, and the distinction between them is not even that easy to draw theoretically. To pick an example close to my neck of the woods (with a surprisingly detailed and accurate Wikipedia entry), non-sequential double ionization of noble gas atoms enables you to distinguish relatively clearly between collisional ionization and collisional-excitation-plus-detachment, but this need not always be the case.

  • As pointed out in the comments, atoms and molecules are intrinsically quantum mechanical objects, so any sort of understanding of collisional ionization that tries to make sense of it using a 'billiard balls' picture of electrons will at best be an approximate picture. In certain regimes (like the NSDI experiments linked to above) this can be a surprisingly accurate approximation, but in general there will be lots of quantum mechanical effects which completely escape explanation via classical mechanics.

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  • $\begingroup$ Electron capture via $A+e^-\to A^-+\gamma$ is possible; Thus no other particle is needed to receive the excess energy. $\endgroup$ – Arnold Neumaier May 20 '16 at 15:45
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    $\begingroup$ @Arnold Right you are. It's just photodetachment in reverse so it needs to be able to happen. Post edited. $\endgroup$ – Emilio Pisanty May 20 '16 at 16:10

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