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If in this case I can consider the photon as a particle, and the electron punctual, then the interior of the atom is apparently an empty place.

I don't know at what minimum distance from an electron a photon can pass without being absorbed by it. It seems to me that photons can pass through an atom without being absorbed.

However, I know that the interior of an atom is complex, because it is quantum, and difficult to understand.

Am I right, or any photon that "tries" to cross an atom will always be absorbed as it passes through it?

Urb
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João Bosco
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    What does minimum distance from an electron a photon mean in this context? Generally speaking, an electron in a bound atomic state does not have a definite position. A photon is more subtle still. Are you picturing classical point particles? – Alfred Centauri Jun 27 '21 at 02:42
  • @Alfred Centauri - I think that an electron and a photon as particles, from a classical or quantum point of view, cannot fill the entire interior space of the atom with their size. – João Bosco Jun 27 '21 at 02:53
  • Related: https://physics.stackexchange.com/q/648041/50583 – ACuriousMind Jun 27 '21 at 13:47
  • If pigs had wings they could fly – Oбжорoв Jun 28 '21 at 09:01

2 Answers2

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One should not confuse a particle with a point-like object. Photons are particles in the sense that they can be counted, have momentum, etc. They are however not point-like. Just like an electron in QM is extended in space, photons are extended in space. Their spatial structure is the mode structure of the electromagnetic field, of which they are excitations. In optical region the wave length of electromagnetic field is a few hundred nanometers, whereas the size of an atom is a fraction of a nanometer. Thus, one cannot meaningfully speak of a "photon passing through an atom".

On the other hand, one does frequently assume that an atom is interacting with an electromagnetic field that is constant in space - in other words, an atom can be viewed as a point-like object. In particular, atoms passing through cavities localuzing electromagnetic field is a rather common experimental and device setup, e.g., in the H-maser.

If we discuss such an atom passing through a cavity, the probability of it absorbing a photon can by calculated as $$ P(\tau) = e^{-\Gamma \tau}$$ where $\Gamma$ is the absorption rate, calculated using the Fermi golden rule, whereas $\tau$ is the passage time, i.e., the time that the atom spends in the cavity. Note however, that using the Fermi golden rule assumes that the transition rate is small, and that the atom does not interact again with the field after emitting/absorbing the photon. If atoms spend long time in the cavity, as in actual masers/lasers, one needs to resort to more complex midels, such as Jaynes-Cummings or, in case of many atoms, Dicke model.

Roger V.
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  • "Just like an electron in QM is extended in space, photons are extended in space. " This sentence is doubly flawed. Here's another: "Their spatial structure is the mode structure of the electromagnetic field, of which they are excitations. " – my2cts Jun 27 '21 at 10:25
  • "one does frequently assume that an atom is interacting with an electromagnetic field that is constant in space." This is unclear. Perhaps you mean a plane wave? – my2cts Jun 27 '21 at 10:25
  • @my2cts electromagnetic field changes little on the scale of atomic size, which is the basis for writing interactions like $\mathbf{d}\cdot\mathbf{E}(t)$. – Roger V. Jun 27 '21 at 10:51
  • So are you indeed talking about the plane wave approximation for optical transitions? – my2cts Jun 27 '21 at 10:55
  • @my2cts regarding your first comment see any standard reference on em field quantization, also Wikipedia: https://en.m.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field – Roger V. Jun 27 '21 at 10:55
  • Can you give precise references for your statements "Just like an electron in QM is extended in space, photons are extended in space. Their spatial structure is the mode structure of the electromagnetic field, of which they are excitations. " ? – my2cts Jun 27 '21 at 11:07
  • @my2cts it doesn't have to a plane wave - the important thing is that field changes slowly on the scale of an atom. Atom is point like, not the field. – Roger V. Jun 27 '21 at 11:11
  • @my2cts I was referring to the fact that first quantization for em field is identical to the second quantization for fermions. Essentially, mode structure of field is the equivalent of the fermionic eigenstates. Note that modes are plane waves only in free space - the procedure works the samein cavities, wave guides, etc. – Roger V. Jun 27 '21 at 11:13
  • An electron is not 'extended' and neither is a photon. The wave function describing them are. Secondly, note that I indeed wrote 'plane wave approximation'. – my2cts Jun 27 '21 at 12:31
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In general there is a finite probability that a photon passes an atom without interaction. The presence of an atom causes matrix elements between electromagnetic waves. The new electromagnetic wave is therefore an expansion of electromagnetic waves. In general the unperturbed wave component has a finite coefficient, the square of which gives the probability of finding photons that pass the atom without interaction.

my2cts
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