View Full Version : Annihilation Question ( Particle-Antiparticle )

joeboo

2005-Mar-22, 09:57 PM

First off, as this is my first post, I'd like to say "Hello". I asked a question of a friend, and he directed me to this forum. I'm a man of many words who would prefer to be a man of few, so I'll just get to the point:

Is there any information, either experimental or theoretical, that would shed light on the maximum distance at which annihilation can occur between a particle and it's antiparticle?

Also, since it's in many ways a similar question, ( and I hope I can say this in a way that makes sense while not seeming trivial ): How long does an annihilation "take to happen" ?

Anyway, thanks in advance to anyone with any information,

-joeboo

antoniseb

2005-Mar-22, 10:40 PM

Originally posted by joeboo@Mar 22 2005, 09:57 PM

Is there any information, either experimental or theoretical, that would shed light on the maximum distance at which annihilation can occur between a particle and it's antiparticle?

Also, since it's in many ways a similar question, ( and I hope I can say this in a way that makes sense while not seeming trivial ): How long does an annihilation "take to happen" ?

Welcome to the UT forum Joeboo.

I do not have a specific answer to your question but the answer will most likely depend on which particles are involved. I would imagine that for electron-positron the distance would probably be about 10 to 100 picometers, whereas for a proton-antiproton we are probably talking about 1 to 10 femtometers. The fact that they have attracting charges and other forces might increase the distance for which it will be assured of happening.

Relative velocity may also be a big factor in changing the apparent cross-section.

As to how long it takes... A very short time.

Why do you ask? We can look it up if its important.

joeboo

2005-Mar-22, 11:44 PM

Originally posted by antoniseb+--></div><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td>QUOTE (antoniseb)</td></tr><tr><td id='QUOTE'>Welcome to the UT forum Joeboo[/b]

Thanks!

<!--QuoteBegin-antoniseb

Why do you ask? We can look it up if its important. [/quote]

The important thing is that it's definitely finite and non-zero ( although this part is largely obvious, you never know ). The specific numbers aren't as important as the knowledge that the absolute minimum duration of annihilation is strictly positive ( in other words, if we were given an infinite number of particle-antiparticle pairs and infinitely precise equipment, would we see annihilations that occured in arbitrarily small time intervals, although positive? Or would they all take at least t seconds, for some t > 0. Similarly, I would like some evidence that these pairs aren't annihilating at arbitrarily large distances. Obviously, we wouldn't expect this, but I can conjure up examples where it's at the very least "remotely plausible". Perhaps I should restate my question in a different light:

Assume we have a particle p and it's antiparticle p_bar that start out at a common point x_0 ( or as close as is possible to common ) at a time t_0, and they are headed in opposite directions ( velocity v>0 and -v resp. ).

Does there exist a distance D > 0, and a time interval I > 0 such that if:

( x_0 + v*I ) - ( x_0 + (-v)*I ) = 2v*I > D

( possibly overlooking some relativistic consideration's in the above formula )

Then we are guaranteed p and p_bar will not annihilate ( each other, assuming they don't cross paths again for some unrelated reason ).

Stated in friendlier prose: If we could find the maximum distance over which an annihilation could occur, and the minimum time in which it could take place, and both were non-zero and finite, then we could essentially find an "Annihilation Escape Velocity".

Am I making any sense?

-joeboo

antoniseb

2005-Mar-23, 12:12 AM

Originally posted by joeboo@Mar 22 2005, 11:44 PM

Am I making any sense?

Yes, you are making sense, and also better establishing the level that you are looking for an answer. I suspect that it is important for the annihilation to happen that the two particles have to encounter each other with their probability functions having antinodes in the same time and place, where as during the virtual creation from a photon, they may have node-antinode placement initially. I am not sure that velocity makes sense at those distances so much as other factors with little or no analog in the macroscopic world.

joeboo

2005-Mar-23, 08:36 AM

antoniseb,

Thank you for your comments thus far.

A few more questions if you ( or anyone else ) don't mind:

I suspect that it is important for the annihilation to happen that the two particles have to encounter each other with their probability functions having antinodes in the same time and place

I understand ... somwhat. However, are there specific probability functions that govern this interaction? ( for reference, I'm a math person, so I'm fond of equations and rigorous definitions )

during the virtual creation from a photon, they may have node-antinode placement initially

I'm assuming from this that the probability function describes some 'potential for interaction' between the 2 particles, and that when the antinodes line up, the probability for interaction is at a maximum? Again, more math would be helpful :)

I am not sure that velocity makes sense at those distances so much as other factors with little or no analog in the macroscopic world.

I'm not sure it matters either, I simply included it as a manner of framing the question. The issue isn't really "how fast do they have to move to avoid annihilation", it's more of "How close do they have to be and for how long". Still, this is far to rudimentary to describe what appears to be ( given my very limited knowledge ) largely a QM problem. Nonetheless, I can't help but wonder if such bounds ( on the distance and duration for annihilation ) can exist..

Thank you, again,

-joeboo

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