Particle / Anti-particle Annihilations

[joeboo]

Are there any experimental or theoretical limits on the distance at which a particle / anti-particle pair ( or pair for short ) can annihilate? If there is, are there any limits on the duration a pair must be within said distance in order for an annihilation to occur?

In other words: Do there exist, at the very least theoretical, conditions under which a colocated ( read: very close ) pair can be guaranteed to separate fast enough to "escape annihilation" ?

I realize this question relies on a great deal more than the simple notions of distance, time and motion, so any reference material would be greatly appreciated.


-joeboo

 

[jtbell]

At the quantum-mechanical level, physicists don't think in terms of distance of closest approach, because you can't think of either particle as having a definite position at any particular time. (Remember the Heisenberg Uncertainty Principle?)

Instead, we think in probabilistic terms, using a quantity called the interaction cross section. If we have a thin target of thickness $dx$, containing $n$ electrons per m^3, and we fire $N_0$ positrons at it, the number $dN$ that annihilate is, on the average,

$$dN = \sigma N_0 n dx$$

where the proportionality constant $\sigma$ is the interaction cross section for annihilation. We can measure $\sigma$ by counting how many positrons actually annihilate, and calculating

$$\sigma = \frac {1}{N_0 n} \frac {dN}{dx}$$

We can also predict $\sigma$ from theory, using quantum electrodynamics. It depends on the energy of the positrons.

A Google search on

electron positron annihilation cross section

turns up a lot of pages, some of which have theoretically-derived formulas for $\sigma$, and others which have the measured values.

 

[R0man]

Particle/anti-particle annihilations occur when a particle and its corresponding anti-particle come into contact and are converted into energy. This process is governed by the laws of quantum mechanics and is well understood through experimental observations and theoretical calculations.

There are indeed limits on the distance at which a particle/anti-particle pair can annihilate. This distance is known as the "Compton wavelength" and is specific to each type of particle. It is determined by the mass of the particle and its energy, and can be calculated using the formula λ = h/mc, where h is Planck's constant, m is the mass of the particle, and c is the speed of light. For example, the Compton wavelength of an electron is approximately 2.4 x 10^-12 meters.

This means that for a particle/anti-particle pair to annihilate, they must come within a distance of at least the Compton wavelength. If they are further apart, they will not interact and will not undergo annihilation. This is an experimental limit, as it has been observed that particles and anti-particles do not interact beyond this distance.

As for the duration a pair must be within this distance for an annihilation to occur, there is no specific limit. As long as the pair is within the Compton wavelength, they can potentially undergo annihilation. However, the probability of annihilation decreases as the duration of their interaction decreases. This is because the longer they are within this distance, the more likely they are to interact and undergo annihilation. So, while there is no specific time limit, the longer the pair is within the Compton wavelength, the higher the probability of annihilation.

It is also worth noting that there are other factors that can affect the probability of annihilation, such as the presence of other particles and the strength of the electromagnetic force. These can also influence the duration and distance at which annihilation can occur.

In summary, there are experimental and theoretical limits on the distance at which a particle/anti-particle pair can annihilate, but there is no specific limit on the duration they must be within this distance for annihilation to occur. As for the possibility of a pair separating fast enough to "escape annihilation," this is not possible within the framework of quantum mechanics. The laws of quantum mechanics dictate that particles and anti-particles will always interact when they come within the Compton wavelength.