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Saado
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How close does does a particle and anti-particle pair have to be with each other in order to achieve annihilation?
Saado said:How close does does a particle and anti-particle pair have to be with each other in order to achieve annihilation?
Close enough for their wave functions to overlap.Saado said:How close does does a particle and anti-particle pair have to be with each other in order to achieve annihilation?
Seems obvious, but actually not! Look at the Feynman diagram, there's two vertices x1 and x2. The electron arrives at point x1 and emits a photon, the positron arrives at point x2 and emits a photon. In between, a virtual particle. The amplitude is obtained by integrating over all x1, x2, but there's no requirement that they coincide.Meir Achuz said:Close enough for their wave functions to overlap.
It's not "my" Feynman diagram. But I appreciate the offer!Meir Achuz said:Your Feynman diagram is for free particles.
"Relevant", I guess, but not accurate. The Feynman diagram approach still works. Just take the result for plane waves and integrate it over the momentum distribution for a bound state. Doesn't change the fact that there are two vertices that need not coincide.Include spatial bound state wave functions in the full calculation, and then "close enough for their wave functions to overlap" is relevant.
P-wave states most certainly do annihilate, even though |ψ(0)|2 = 0. However the rate is suppressed by the usual factor for the centrifugal barrier, (p/mc)2L, since the particles spend more of their time farther apart.That is why P waves don't annihilate, but S waves do, with the rate proportional to |\psi(0)|^2
Bill_K said:P-wave states most certainly do annihilate, even though |ψ(0)|2 = 0. However the rate is suppressed by the usual factor for the centrifugal barrier, (p/mc)2L, since the particles spend more of their time farther apart.
For a p-wave, L = 1, this factor is basically v2/c2, or the ratio of the potential energy to the rest energy, 6 eV/0.5 MeV, about 10-5. Instead of nanoseconds, the lifetime for p-wave annihilation is therefore in the microsecond range. But the radiative decay to s-wave via electric dipole transition takes place in 10-8 sec. So the direct annihilation from p-wave is perfectly possible, but has too small a branching ratio to be observed.
Minimum distance for annihilation refers to the shortest distance at which particles or antiparticles can come into contact and annihilate each other, resulting in the production of energy in the form of photons or other particles.
Understanding the minimum distance for annihilation is crucial in various fields of physics, such as particle physics and astrophysics. It helps us determine the conditions necessary for particles and antiparticles to annihilate, and it provides insight into the fundamental forces and interactions at play.
The minimum distance for annihilation is determined by the size and energy of the particles involved, as well as the strength of the forces between them. It can be calculated using mathematical models and experimental data.
The minimum distance for annihilation is a fundamental property of particles and cannot be altered. However, the conditions under which annihilation occurs, such as the presence of other particles or high energy collisions, can affect the distance at which it takes place.
Other phenomena related to the minimum distance for annihilation include pair production, where particles and antiparticles are created from energy, and nuclear reactions such as fusion and fission, which involve the annihilation of particles within atomic nuclei.