## The meaning of Ionization

What is the definition of ionization? For example, in the case of Hydrogen atom, the Coulomb force is the long-range, so the electron and its wave function is always affected by the left proton. So the QUANTUM description is actually difficult and unclear.

Could anyone explain to the the meaning of Ionization from the quantum perspective?

Forget about the Quantum tunneling, it doesn't solve the problem I have mentioned above.
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 The electron has escaped away. So only the proton of the Hydrogen atom is left.

## The meaning of Ionization

From any perspective, quantum or otherwise, ionization is when the electron gains enough energy that it's no longer bound to the nucleus. If the electron is a distance r away from the rest of the atom, it's potential energy is $$V(r) = -\frac{1}{4 \pi \epsilon_0}\frac{e^2}{r}$$. Ionization has occurred when the electron's total energy is positive, which will mean that it's free to move anywhere without failing to conserve energy. So, it's kinetic energy must be no smaller than $$-V$$.

 Quote by Quantum River What is the definition of ionization? For example, in the case of Hydrogen atom, the Coulomb force is the long-range, so the electron and its wave function is always affected by the left proton. So the QUANTUM description is actually difficult and unclear. Could anyone explain to the the meaning of Ionization from the quantum perspective? Forget about the Quantum tunneling, it doesn't solve the problem I have mentioned above.
Well, the ionization energy is defined as the energy necessary to remove an electron from the neutral atom.

So why are you talking about protons that "have left" ?
Besides, you are claiming that QM cannot explain ionization ? If so, you really need to start doing some thorough studying, my dear. You might just wanna start with how electronic energylevels in atoms are described by QM. Leave the "tunneling" for what it is and first start with the basic concepts.

marlon
 I didn't claim QM couldn't explain ionization. My viewpoint is you are explaining the ionization from a classical (physics) point. Could you remove the electron from the neutral atom? The removed electron (for example the center of the wave function is now 10 nm from the original neutral atom) is still affected by the atom from a quantum point, because the wave function of the electron appears in every point of the space and the Universe. Of course you can approximate that distribution of the wave function is concentrated in a narrow place (for example some small ball with a radius of 1 nm) and so the influence of the original atom will not be taken into account. But it is just an approximation and under many circumstances this approximation will not work any more. I just want to say because of the long-range nature of the coulomb force. The concept of the Ionization is somewhat not exact as you may assume.

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 Quote by Quantum River I didn't claim QM couldn't explain ionization. My viewpoint is you are explaining the ionization from a classical (physics) point. Could you remove the electron from the neutral atom? The removed electron (for example the center of the wave function is now 10 nm from the original neutral atom) is still affected by the atom from a quantum point, because the wave function of the electron appears in every point of the space and the Universe. Of course you can approximate that distribution of the wave function is concentrated in a narrow place (for example some small ball with a radius of 1 nm) and so the influence of the original atom will not be taken into account. But it is just an approximation and under many circumstances this approximation will not work any more. I just want to say because of the long-range nature of the coulomb force. The concept of the Ionization is somewhat not exact as you may assume.
So can you show me any effects of the gravitational field from Alpha Centauri in the dynamics of what we observe here on Earth? Do you detect it when you drop a ball, or any other experiment?

Now apply this to a plasma. Can you show what observations of the property of such a plasma that would support your arguments? For example, there were two recent laser-plasma wakefield experiment as an accelerating mechanism[1,2]. In which part of these two experiments would the "long range coulomb force" of the ionized atom with its separated electron played any role in the description of the physics?

Zz.

1. W P Leemans et al. Nature Physics v2, p699 (2006).
2. J Faure, et al, Nature v444, p737 (2006).

Zz.
 I have read Faure's paper and it is interesting. The laser field and wakefield both have a electric field>100GV/m, which is comparable with the Coulomb field when the electron has a distance of one Bohr radius with the atomic nucleus. So I guess the Coulomb force may play a noticeable role in the process of ionization, although plasma physicists will not taken into account the Coulomb force and the subsequent quantum effects at all. Once the electron has been removed from the atomic nucleus, the Coulomb force will be relatively small compared with the laser electric field. I guess the nucleus may play a role like the nucleus in the Rutherford alpha scattering. So the energy width (in Faure's experiment, the energy spread is 20%-5%) is partly contributed by the existence of atomic nucleus. Quantum River

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 Quote by Quantum River I have read Faure's paper and it is interesting. The laser field and wakefield both have a electric field>100GV/m, which is comparable with the Coulomb field when the electron has a distance of one Bohr radius with the atomic nucleus. So I guess the Coulomb force may play a noticeable role in the process of ionization, although plasma physicists will not taken into account the Coulomb force and the subsequent quantum effects at all. Quantum River

Neglecting spin effects, the Coulomb "force", better call it "interaction" plays the SINGLE POSSIBLE role in the process of ionization. So instead of "may play", i'd rather say "plays".

Daniel.

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 Quote by Quantum River I have read Faure's paper and it is interesting. The laser field and wakefield both have a electric field>100GV/m, which is comparable with the Coulomb field when the electron has a distance of one Bohr radius with the atomic nucleus. So I guess the Coulomb force may play a noticeable role in the process of ionization, although plasma physicists will not taken into account the Coulomb force and the subsequent quantum effects at all. Once the electron has been removed from the atomic nucleus, the Coulomb force will be relatively small compared with the laser electric field. I guess the nucleus may play a role like the nucleus in the Rutherford alpha scattering. So the energy width (in Faure's experiment, the energy spread is 20%-5%) is partly contributed by the existence of atomic nucleus. Quantum River
YOu did not read the same paper, nor did you understand it.

The wakefiled is created NOT by the coulombic attraction between the ionized atom and its separated electron. Read the physics carefully. Rather, the accelerating gradient is created by regions of charges where the is an accumulation of FREE charges, which is called the blowout region of the plasma. You do NOT get that kind of a field gradent between an electron an a positively ionized atom when they are already separated! If you think this separated distance is the Bohr radius, then you haven't understood what they were doing.

Also note that the accelerating gradient that is being quoted is the gradient being felt by the electrons being accelerated, NOT the gradient between the ionized atom and the separated electron. No such physics is ever considered in the wakefield experiment. In fact, the physics involved contains a complete separation of the elctrons and the ions (again, the blowout regime). This is the fundamental mechanism of laser-plasma acceleration.

Zz.
 The wakefiled is created NOT by the coulombic attraction between the ionized atom and its separated electron. Did I say the wakefield was created by the coulombic attraction. Read the physics carefully. Rather, the accelerating gradient is created by regions of charges where the is an accumulation of FREE charges, which is called the blowout region of the plasma. You do NOT get that kind of a field gradent between an electron an a positively ionized atom when they are already separated! If you think this separated distance is the Bohr radius, then you haven't understood what they were doing. I am so luck to think that their separated distance is not the Bohr radius. Also note that the accelerating gradient that is being quoted is the gradient being felt by the electrons being accelerated, NOT the gradient between the ionized atom and the separated electron. No such physics is ever considered in the wakefield experiment. In fact, the physics involved contains a complete separation of the elctrons and the ions (again, the blowout regime). This is the fundamental mechanism of laser-plasma acceleration. Actually I have said the Coulomb force plays a noticeable role in the process of ionization and it may still play a role after the ionization because the electron still could collide with the atomic nucleus after the ionization.

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 Quote by Quantum River The wakefiled is created NOT by the coulombic attraction between the ionized atom and its separated electron. Did I say the wakefield was created by the coulombic attraction.
You implied! You quoted the wakefield gradient and said that it is the field at a distance of Bohr radius. This association is misleading at best, and wrong at worst. The high gradient is created by the large amount of charges that have been segregated in regions that are separated by at least equal to the wavelength of the laser. This is many, many times larger than the Bohr radius.

 Read the physics carefully. Rather, the accelerating gradient is created by regions of charges where the is an accumulation of FREE charges, which is called the blowout region of the plasma. You do NOT get that kind of a field gradent between an electron an a positively ionized atom when they are already separated! If you think this separated distance is the Bohr radius, then you haven't understood what they were doing. I am so luck to think that their separated distance is not the Bohr radius. Also note that the accelerating gradient that is being quoted is the gradient being felt by the electrons being accelerated, NOT the gradient between the ionized atom and the separated electron. No such physics is ever considered in the wakefield experiment. In fact, the physics involved contains a complete separation of the elctrons and the ions (again, the blowout regime). This is the fundamental mechanism of laser-plasma acceleration. Actually I have said the Coulomb force plays a noticeable role in the process of ionization and it may still play a role after the ionization because the electron still could collide with the atomic nucleus after the ionization.
But this is what TYPE of coulomb force, and why would this be relevant to what you insisted in the OP? The existence of this accelerating gradient is simply due to the segregation of those charges. The PHYSICS that describes them have nothing in it that contains a coupling, even weakly, between the electrons and the ions, which you insisted must still be there. Yet, you latched on to this example which I brought up as if it justifies what you are arguing. This is incorrect.

I brought up this example because this is exactly the type of area that I work in, except that I generate wakefields in dielectric structures. So I deal with the physics and experimental measurements of such things daily. When I hear people make claims of something that simply do not jive with a whole field of study, then something has been seriously overlooked. You cannot make unjustified claim without showing valid experimental evidence, which I have requested that you do and haven't provide. I, on the other hand, can provide a few more (photoionization, secondary electron emission, etc.) to counter your claim.

Zz.
 Please calm down guys, all the red text and quotes hurt my eyes. Has anybody answered the original question? I don't see any difficulty in interpreting the original post, it seems like a simple enough question to me. I don't see that he is claiming that quantum physics fails to explain ionisation, or that there are any significant effects... I am interested if by seperating a proton and electron it is possible to stop their wave functions from overlapping... if they must always overlap then, presumably, there must always be some non-zero probability that an ionised atom is actually neutral, or is going to become neutral very soon. So, how do we define ionisation in quantum terms? Must it necessarily be fuzzy like so many other quantities? Can we decide exactly when an electron is free and when it is not? Can we label atoms as exactly ionised without introducing some error (maybe really small)?

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 Quote by Jheriko Has anybody answered the original question? I don't see any difficulty in interpreting the original post, it seems like a simple enough question to me. I don't see that he is claiming that quantum physics fails to explain ionisation, or that there are any significant effects... I am interested if by seperating a proton and electron it is possible to stop their wave functions from overlapping... if they must always overlap then, presumably, there must always be some non-zero probability that an ionised atom is actually neutral, or is going to become neutral very soon.
But I can already verify this by assuming the negative. IF we can't remove the overlap, then we will never have such thing as free charges. Then all of what we have assumed to be free charges are really not free. If that is the case, then there will be some "new" physics that we should be seeing that isn't part of physics that we're using to describe the system. Where are they?

That is what I have been asking when I cited the plasma wakefields. The physics describing such a system explicitly assumes that the electrons and the ions are not coupled other than "globs of electrons" and "globs of ions" producing E-field. Another such example would be simply the photoelectric effect. When the electron IS coupled to the ions, you get the work function. But when it overcomes that, there are no interaction of any kind with the original solid and you get free electrons. To argue if we still any "overlap", to me, is rather puzzling when the description that we have of the photoelectron as free particles unthetered to the original atom/solid works! The same can be said with photoionization phenomenon.

This is what I've been asking. Is there any observation to indicate otherwise?

Zz.
 Recognitions: Science Advisor Quantum River -- First, ionization has been around for a very long time. In other words it is a well accepted phenomena, and, indeed, a well understood phenomena. check out a chemistry book or two, check out biological work -- free radicals and all that -- ions are big trouble in air pollution. Second -- review your knowledge of the H atom. There are two types of solutions. One type describes the well known bound states. The other describes scattering states. So when something disturbs a normal H atom enough for a transition from bound to scattering, then, voila, you've got your basic ionization process. Check out photoelectric and photo-ionization phenomena. Further note that the a basic phenomena in the details of human vision involves some ionization -- photoinonization of rhodopsin by a photon --. Don't forget the ozone layer. Read up on atomic and molecular physics -- these ionization issues have been settled for a very long time. Again, in QM, ionization is directly associated with transitions from bound to continuous states. If you are worried about distance, study the problem with wave packets. Regards, Reilly Atkinson

 Quote by Quantum River What is the definition of ionization? For example, in the case of Hydrogen atom, the Coulomb force is the long-range, so the electron and its wave function is always affected by the left proton. So the QUANTUM description is actually difficult and unclear. Could anyone explain to the the meaning of Ionization from the quantum perspective? Forget about the Quantum tunneling, it doesn't solve the problem I have mentioned above.
If the removed electrons couldn't have the possibility to interact with something else outside the atom, your consideration could have some meaning, but of course, it's not this the case.

 Quote by ZapperZ But I can already verify this by assuming the negative. IF we can't remove the overlap, then we will never have such thing as free charges. Then all of what we have assumed to be free charges are really not free. If that is the case, then there will be some "new" physics that we should be seeing that isn't part of physics that we're using to describe the system. Where are they?
I don't really undeerstand this. For me it just means that the contributions from overlapping are either unobservably small or that overlapping is forbidden. I think I must be misunderstanding you somehow...

If I apply what I think is your logic then there should be new physics on Earth. We ignore the gravitation of distant astronomical objects when making calculations, but if this gravitation really effects us there should be some new physics? We don't remove the 'overlap' in the case of gravitation... it is just neglected since it makes no observable difference to the results of our calculations.

So, my original question still stands: is the overlapping forbidden?