Matter/Antimatter Collision Radius

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    Collision Radius
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Discussion Overview

The discussion revolves around the concept of matter and antimatter collisions, specifically addressing the minimal distance required for such a reaction to occur and the implications of particle behavior as wave-packets. Participants explore the definitions of "collision" in the context of quantum mechanics and the role of the Heisenberg uncertainty principle in determining interaction probabilities.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the minimal distance for a matter-antimatter collision could be considered zero, as suggested by the Feynman diagram representation of particle interactions.
  • Others argue that the concept of wave-packets implies that particles do not collide in a traditional sense, but rather there is a probability of interaction based on the overlap of their wave-packets.
  • A participant mentions specific cross-section data for positron-electron and antiproton-proton interactions, indicating that these values vary with energy levels.
  • There is a discussion about the influence of the Heisenberg uncertainty principle on the finite cross-section of interactions, with some questioning its sufficiency as the sole factor.
  • One participant expresses confusion regarding how a zero minimum distance could allow for reactions to occur, questioning the implications of such a distance on interaction probabilities.
  • Another participant suggests that the maximum distance for interaction could be infinite, although the probability of interaction would decrease significantly with distance.

Areas of Agreement / Disagreement

Participants express differing views on the nature of particle collisions, the implications of wave-packet behavior, and the factors influencing cross-sections. The discussion remains unresolved with multiple competing perspectives on these topics.

Contextual Notes

Limitations include the dependence on interpretations of quantum mechanics, the ambiguity in defining "collision," and the unresolved nature of how various factors contribute to interaction probabilities.

Jonnyb42
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I am curious, if a matter particle and it's corresponding antimatter particle meet, they will annihilate to produce pure energy. Which is the minimal distance between the particles that would allow the reaction to occur and how is that determined? (I ask this because I know that the nice idea of thinking of particles as spheres with boundaries is false, so then what is the definition of "collide" if you know what I mean?)

Asked another way; If there are no true boundaries to a particle (and if I am mistaken, let me know) how can two "collide"? (not so much in an electromagnetic repulsion, but more specifically regarding matter/antimatter collisions)
 
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For fast positrons annihilating with electrons at rest, the annihilation-in-flight probability plot is shown on page 274 and 385 of Heitler "Quantum Theory of Radiation" 3rd edition. The cross section is maximum near 0.5 MeV. The cross section, derived in section 27 (page 268), is originally attributed to P.A. M. Dirac (1930). According to Heitler, "... in most cases, a fast positron will first lose all its energy and is then annihiliated [at rest]".
For antiprotons annihilating on protons, see the plots for p-bar p and pp total cross sections in Fig. 40.11 in
http://pdg.lbl.gov/2009/reviews/rpp2009-rev-cross-section-plots.pdf
The total cross sections for p-bar p (anti-proton annihilation) and pp are nearly equal above 10 GeV, and between 40 and 100 millibarns (slightly above geometric; ~pi R2). Below 10 GeV, the p-bar p cross section rises above 300 millibarns.
Bob S
 
Bob S, I don't think the OP was asking about cross sections. I think the simple answer to his question is zero. The Feynman diagram for this process has the world-lines of the particle and antiparticle intersecting at a point. The reason you get a finite cross-section, even though the range of the effect is zero, is the Heisenberg uncertainty principle; each particle is a wave-packet that covers a certain amount of space.
 
bcrowell said:
Bob S, I don't think the OP was asking about cross sections. I think the simple answer to his question is zero. The Feynman diagram for this process has the world-lines of the particle and antiparticle intersecting at a point. The reason you get a finite cross-section, even though the range of the effect is zero, is the Heisenberg uncertainty principle; each particle is a wave-packet that covers a certain amount of space.
Why is the p-bar p interaction probability larger than the pp interaction probability at GeV energies, if the finite cross section is due only to the Heisenberg uncertainty principle?
Bob S
 
I am a little confused, if each particle is a wave-packet that covers a certain amount of space, how can the minimum distance of a particle/antiparticle collision be zero? Also, if this distance were zero, how could these reactions ever occur? If they have to be at no distance with each other wouldn't such a reaction have zero probability of occurring?
 
Here's a rough way of thinking about it: when you think about particles as wavepackets, they don't really "collide." Rather, there is some probability that the two particles will disappear and be replaced with one or more new particles. This probability is related to the "overlap" (a term that I am intentionally using vaguely) of the two wavepackets. When the wavepackets are closer together, the probability of an interaction becomes larger.
 
Ooh i see, that is cool. Also i realized I meant to ask what is the MAXimum distance between them, but after your explanation I guess it would be infinity, except the probability would be very low. (Am I right?)

Thanks
 
Bob S said:
Why is the p-bar p interaction probability larger than the pp interaction probability at GeV energies, if the finite cross section is due only to the Heisenberg uncertainty principle?
Bob S

I didn't say that the H.u.p. was the only factor in determining the cross section.
 

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