Question on electron-photon interaction scattering

[Argos]

Reading the brilliant discussions on Compton effect led by J. Kierien, JS Princeton, Zathras, Tim Thompson, and many others, A question on electron-photon interaction scattering came to my mind, and I hope some of you guys could answer. As I donīt want to contaminate those high profile discussions with silly interventions I started a new one.

What happens if I make constant flowing [this should provide a high number of scatterings] electron and ultra-violet beams to cross at, say, 90 degrees?

Will I obtain a beam of lower energy [visible] photons emitted from the point of intersection of the beams? If this were true, what would be the scattering angle of the emitted beam? Will it be emitted in all directions, or will the direction of propagation of the beam vary slightly and constantly due to quantum fluctuations, constrained to something like a cone shape propagation volume?

[Argos]

Well, after 16 views, including JKīs, I just have to conclude that the question is meaningless, neglectable, non-sense, or something worse.

Pardon me for asking. [img]/phpBB/images/smiles/icon_smile.gif[/img]

[Zathras]

On 2003-02-07 08:08, Argos wrote:
Reading the brilliant discussions on Compton effect led by J. Kierien, JS Princeton, Zathras, Tim Thompson, and many others, A question on electron-photon interaction scattering came to my mind, and I hope some of you guys could answer. As I donīt want to contaminate those high profile discussions with silly interventions I started a new one.

What happens if I make constant flowing [this should provide a high number of scatterings] electron and ultra-violet beams to cross at, say, 90 degrees?

Will I obtain a beam of lower energy [visible] photons emitted from the point of intersection of the beams? If this were true, what would be the scattering angle of the emitted beam? Will it be emitted in all directions, or will the direction of propagation of the beam vary slightly and constantly due to quantum fluctuations, constrained to something like a cone shape propagation volume?

The first thing to do is look at the energy region you are in. UV photons have energy on the order of 10eV, while electrons have a rest energy of 511 keV. Since the photon energy is much less than the energy of the electron, one can look at the "classical" Thompson scattering limit.

You want to look at the impact when the two beams are at 90 degree angles with respect to each other, presumably in the lab frame.

One question you must look at is the polarization of the photons. If the photons are uniformly polarized in one way, you will get a different scattering pattern than if they are not polarized.

Quantum fluctuations would not be a problem, if you have the steady beam you are discussing.

With respect to the scattering probability for the photons, that depends of the density of the electron beam as well as its size. The probability of scattering can be approximated as (n*sigma*r), where n is the number density of electrons in the beam, sigma is the integrated scattering cross section (on the order of 10e-14 m) and r is the radius of the beam. You would have to have an extremely dense and/or thick beam in order to get the majority of them scattered, and it would be extremely difficult to collimate such a beam. Therefore, a large majority would go all over. As for those that are scattered, any direction is possible, but the relative probabilities for each angle will depend on the polarization angle. Also, the velocity of the electrons will come into play here, as the calculations are usually done in the electron's rest frame. Therefore, the electron's momentum will "drag" the scattering pattern with it and skew the observations in that way. But again, most will not scatter.

I hope that helps. Post any more questions you might have.

[Zathras]

On 2003-02-07 11:12, Argos wrote:
Well, after 16 views, including JKīs, I just have to conclude that the question is meaningless, neglectable, non-sense, or something worse.

Pardon me for asking. [img]/phpBB/images/smiles/icon_smile.gif[/img]

The question is good; don't apologize.

BTW: how can you tell who has viewed a thread?

[Thumper]

On 2003-02-07 11:28, Zathras wrote:
BTW: how can you tell who has viewed a thread?

Zathras, if you are on the page listing all the threads, you see across the top column headings: Topic, Replies, Poster, Views, Date. Topic is obvious, Replies is the number of individual posts responding to the OP. Poster is the OP. Views is the number of times that thread has been accessed. And Date is the date and time of the last reply along with the author of that reply.

It took me a while to figure out what that all meant. I would never have guessed that I would have been able to make even a semi relevant post in this thread.

(typos)

<font size=-1>[ This Message was edited by: Thumper on 2003-02-07 12:17 ]</font>

[David Hall]

Yeah, but the question still stands. How can you tell who has viewed your topic, as in the names of people who haven't posted, just looked?

[Argos]

Thank you very much, Zathras. You rescued me from feeling a jerk, with terrible consequences to my egoīs health. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Indeed Iīm surprised that I could put the question in terms, since Iīm not a specialist in the field, just an interested individual, dazzled by particle physics. Iīm still having my share of stony ground with the scattering-related maths. You show having understood acutely the point.

The first thing to do is look at the energy region you are in. UV photons have energy on the order of 10eV, while electrons have a rest energy of 511 keV. Since the photon energy is much less than the energy of the electron, one can look at the "classical" Thompson scattering limit.

In fact Iīm interested in generating visible photons out of an interaction between electrons and higher energy photons [in the lab]. I thought of using UV versus Electrons, so that the higher energy UV scattered into photons of visible wavelengths. I donīt know if such interaction is possible. The energy limits have to be evaluated. I would have to control the energy of the electrons and the photons such as to result in scattering in the adequate wavelengths. Got to check out the feasibility [maybe too much of a load for my little cart].

With respect to the scattering probability for the photons, that depends of the density of the electron beam as well as its size. The probability of scattering can be approximated as (n*sigma*r), where n is the number density of electrons in the beam, sigma is the integrated scattering cross section (on the order of 10e-14 m) and r is the radius of the beam.

Donīt you think that if I could make a polarized beam to sweep through the cross-section of the electron beam, the probability of scattering would be higher?

You would have to have an extremely dense and/or thick beam in order to get the majority of them scattered, and it would be extremely difficult to collimate such a beam. Therefore, a large majority would go all over. As for those that are scattered, any direction is possible, but the relative probabilities for each angle will depend on the polarization angle

Could I make it with an ordinary TV set electron cannon? Thatīs all my budget allows for. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Also, the velocity of the electrons will come into play here, as the calculations are usually done in the electron's rest frame. Therefore, the electron's momentum will "drag" the scattering pattern with it and skew the observations in that way.

Do you mean that, in order to detect the resulting scattered visible photons one will have to compensate for this skewing, translating it into additional degrees of scattering?

But again, most will not scatter.

If I had a constant flow of photons as in a beam, wouldnīt it be reasonable to suppose that at least Iīd have one scattering every, say, 0.0001 sec, in the point of intersection of the mentioned beams, resulting in an apparently steady source of visible light?


In time:

As to “tracking” the posts, there is nothing to it: I saw that JK posted a new topic after I put mine. Titles were side-by-side. Since he is one of the Compton scattering specialists of the board, it would be very unlikely that he left something with the key-word “scattering” to pass unnoticed. Therefore, he should have seen my post.

Regards.

<font size=-1>[ This Message was edited by: Argos on 2003-02-07 14:15 ]</font>

[Zathras]

On 2003-02-07 13:24, Argos wrote:
. . .
In fact Iīm interested in generating visible photons out of an interaction between electrons and higher energy photons [in the lab]. I thought of using UV versus Electrons, so that the higher energy UV scattered into photons of visible wavelengths. I donīt know if such interaction is possible. The energy limits have to be evaluated. I would have to control the energy of the electrons and the photons such as to result in scattering in the adequate wavelengths. Got to check out the feasibility [maybe too much of a load for my little cart].

UV light will not change into visible light unfortunately, because it is not energetic enough to have a large change in energy. The relationship is that the change in the wavelength is equal to h/(mc)*(1-cos(theta)), where m is the mass of the electron and theta is the scattering angle in the frame of the electron. By this formula, the wavelength of light will only change by a fraction of a nanometer, and therefore, the change in energy will be almost undetectable.

Think of it this way: when a tennis ball bounces off a wall, the magnitude of its momentum and kinetic energy will be almost exactly the same as before. The reason for this is that the wall is so massive that the tennis ball will hardly disturb it at all. It is the same thing in the photon-electron example: the electron has so much more energy than the photon that the photon will effectively just bounce off, and the electron will hardly notice it was ever there.

. . .
Donīt you think that if I could make a polarized beam to sweep through the cross-section of the electron beam, the probability of scattering would be higher?
. . .
Could I make it with an ordinary TV set electron cannon? Thatīs all my budget allows for. [img]/phpBB/images/smiles/icon_smile.gif[/img]

For the polarized beam, if I recall correctly, the overall scattering probability will remain the same, but the probability of large scattering angles will (I think increase).

As for the CRT electron gun, I don't know all the numbers, but I am sure that almost all of the photons will go through undisturbed. You will certainly get some scattering, however.

Do you mean that, in order to detect the resulting scattered visible photons one will have to compensate for this skewing, translating it into additional degrees of scattering?

Yes, but with the example of the CRT electron gun, such "dragging" will be minimal, because v << c.

If I had a constant flow of photons as in a beam, wouldnīt it be reasonable to suppose that at least Iīd have one scattering every, say, 0.0001 sec, in the point of intersection of the mentioned beams, resulting in an apparently steady source of visible light?
. . .

You'll have many more scattering than that. You should be able to use the formula I gave previously to determine the scattering probability. Multiply by the number of photons incident on the electron beam, and you'll get a high "number" of scatterings. You'll need a lot to be able to see them however, and I don't know how visible it will be.

<font size=-1>[ This Message was edited by: Zathras on 2003-02-07 14:38 ]</font>

[Argos]

Thanks again, pal. [img]/phpBB/images/smiles/icon_wink.gif[/img]