The meaning of Ionization

ZapperZ

At some point, the inclusion of every single possible effects on the description of a system becomes absurd. I'm sure even you would understand that.

Let's say I only include the strongest possible forces in a system. If what I do not include actually does make an effect, then my descrption of the system using what I started with will reveal "new" stuff that I could not account for. This is what I would call "new physics", something that I never accounted for with my description.

For example, if I drop a ball from rest and only describe this using gravitational forces, then the dynamics of the ball should be completely described by the relevant forces. However, if I start doing this very carefully, and my ball has flaps, then I will notice that my description of the system isn't quite right. It didn't fall at the time that I expect it to. Why? Because the formulation that I used didn't take into account air friction in which, for this sytem and for the accuracy that I want, will now rear its effects that I can no longer ignore, which is not part of the description that I had. If I were ignorant about air friction in the first place, then this is "new physics" that I never realized before.

That is what I asked for. If there truly are effects due to such overlap in system where the description of it completely ignored such effects, were are they? In a photoemission experiment, for example, where the resolution of the electron analyzers are getting to be extremely fine, where would the ignoring of any kind of overlap of the photoelectrons with the atoms in the cathode manifest it effects? Where would such effects reveal themselves in plasma physics?

Note that it is not as if we don't know, or can't tell, when the approximation we make isn't adequate. The "free electron gas" model for a conductor, for example, is quite adequate to explain most of the behavior of an ordinary conductor, such as Ohm's Law. However, we also start seeing breakdown of this model under certain conditions, and for strongly-correlated electron systems, the "overlap" not only between electrons and ions of the solid, but also between electron-electron can manifest itself as a noticeable effects. This forces us to reformulate how we describe such a system, and take into account the necessary interactions.

So yes, we do have experience in dealing with situation where our description is inadequate. In fact, that is what physicists do for a living. That is why I asked for where such a thing would occur and be observable already. Simply by pointing out that the mathematical description of coulomb's law is infinite in range is pointless when its presence cannot be detected or no longer relevant beyond a certain range. I asked for examples where such omissions DO make a difference.

Zz.

reilly

Here we go again. For physics, ionization is not, repeat not, rocket science. I mentioned above, ionization`is and has been understood for a very long time.(How about second semester of a first graduate level course in QM) And, surprise, classical physics does not play a role -- any more than it does in radioactive decay(which can produce ions)

For example, see Chapter 11, section 2.2, p 232 and on, in Mott and Massey's classsic, The Theory of Atomic Collisions, Oxford U. Press, 1933, Yes, 1933. They give a quite thorough discussion of ionization. Also see Linus Pauling's classic General Chemistry, 1947. If I was still teaching, I'd assign each student to find three references on ionization, and write a short paper thereon.

I'd say end of story, except that ionization continued to be an important phenomena in cosmic ray physics, and particle physics prior to WWII, and even through the early 1950s. Why? (There are famous pieces of equipment used then and now that might be related to ionization......)

Those who neglect history are, in physics, very likely to get things wrong.
If there's one thing that bothers me about many posts in this Forum, it is a remarkable ignorance of science history, with elaborate discussions about things that are clearly discussed in the literature. With all due respect, this thread is a good example of what I'm talking about.

Sorry 'bout that.

Regards,
Reilly Atkinson

By the way, just for completeness, an ion is an atom with net non-zero electric charge. Why, every time you breath you take in a few ions -- what kind?

Jheriko

Sorry about all of the confusion, but this is where I misinterpreted you. By new physics I assumed you meant some new physical law(s), rather than having more accurate starting/boundary conditions, but using the same laws. Personally, I would say both systems have the same physics, since they are described by the same laws and would instead use a less ambiguous term like "new phenomena" to describe the effects of having more detailed starting/boundary conditions.

So I guess that the wave-functions overlap, but the contribution towards any effect are neglible in practice?

I apologise if I am ignorant of the history of Physics, I am mostly self-taught and most of the literature I have access to is online... so you are most probably correct that I am ignorant in that respect.

Still, I felt that the original question from the original post was perfectly valid... regardless as to what the history of a subject is or how well documented it is, that doesn't change the validity of a question, nor the fact that nobody gave a simple answer.

ZapperZ

I disagree. Here is the OP:

I believe the question HAS been answered, and answered several times. I have mentioned photoionization (there's a well-established physics for this description), and here's something from reilly:

Now, that may not be "simple" to you, but it is as simple of an answer as one can gets IF one understands that (i) atoms have bound states that are discreet and (ii) free particles have unbounded states that are continuous. So there IS a distinct difference in the description of those two different situations.

This is why I asked, if our description of free particles as unbound, continuous states is inaccurate due to some "overlap" or influence from the original atom, then were would this manifest itself? To simply say something is too small that it simply can't be detected is, frankly, irrelevant.

Zz.

reilly

For all practical purposes, the Coloumb force is the only force in play in the standard treatment of ionization -- basically inelastic scattering of a charged particle and an atom. That is to say, nuclear forces do not play a role in ionization -- unless it is the nucleus itself that undergoes a change in charge. So, Coloumb does the job, quite nicely in fact. Indeed, if an incident electron is the "kicker " then there is a bit of a complication -- the Pauli Principal -- and the choices of using free or Coloumb scattering states to describe the electrons. If the incident electron -- or any particle -- has an energy fairly large compared to the binding energy, then the Born approximation with standard plane wave states will work just fine.

At lower energies, the computations get tricky because the problem becomes a three-body scattering one-- that is, here, with two particles in the final state -- sometimes the issue is termed "final state scattering".

It's a good first year QM problem, at least in the Born approximation -- the initial state is bound electron + nucleus + incident particle --> nucleus + electron + scattered incident particle. You can get reasonable estimates of the probability with a damped exponential wave function for the bound electron, and standard plane waves for the initial and final particle and the outgoing electron. (Just to be clear, to take into acount the "left proton" you must use continuous Coulomb wave functions. A good exercise -- at what energy does the use of a plane wave, rather than a coloumb one, make less than a 5% error in the Born approximation?)

An ionized hydrogen atom is our old friend, the proton. And, the description of ionization in QM is perfectly straightforward -- as I mentioned above, we've had 70+ years to deal with any ambiguities in the basic description of ionization. This is not to say that we know everything about the process, but what we don't know has, so far, failed to cause any problems. Remember that, for example, both the mu and pi mesons were discovered by means of ionization processes -- what was the experimental equipment involved?
Regards,
Reilly Atkinson

Quantum River

I have another two problems concerning ionization.

First, has the physical mechanism of non-sequential ionization been understood clearly?

Second, I must point out the Coulomb kind of force is totally unique because V(r)~1/r. Maybe when V(r)~1/r^(1+$) (where $>0 is some small real number), the physical picture is much clearer.

Think about it, when the main quantum number n of hydrogen is 100, the radius of the electron is 0.53 micrometre and the energy is -1.36 milli-eV. Is the hydrogenic Rydberg atom just a proton with an ionized electron?

Quantum River

ZapperZ

What is an "ionized electron"?

Secondly, under what condition do you often get a hydrogen atom in an excited n=100 state? I mean, since you are so focused on such high quantum number already, why don't you figure out how EXACT it is to get to that particular state AND how far away is the vacuum level!

Thirdly, what does a small variation in the coulomb force have any relevance here? Adding an infinitesimal term to the coulomb force would make a difference to an electron that's a meter away from the ionized atom? Furthermore, what exactly is the point in such a hypothetical scenario in the first place? And what is so unique about it? A gravitational potential also has a 1/r dependence!

Zz.