# How close does a particle-antiparticle pair need to be for annihilation to happen?

I've most often seen the statement that the annihilation of a particle and its antiparticle occurs when they 'collide' with one another. So in other words when they get very close to one another right?

How close do they need to be (for annihilation to occur)?

Charged normal/anti particles will naturally attract one another and lead to such a collision, but I imagine that non-charged pairs could be in some manner coaxed within close proximity - and short of a collision. In this situation can 'annihilation' be moderated to control the rate at which the energy is released, or does annihilation always occur as a sudden and full release of energy?

I did find a question very similar to my question here:

If atoms never "physically" touch each others, then how does matter-antimatter annihilation happen?

But it doesn't directly answer my main question nor the question of whether the annihilation event can be moderated.

A particle isn't really a point particle; its position is best described by a wavefunction: the probability of finding it in any particular region in space.

For annihilation to occur the wavefunctions of the two particles have to overlap - and to the extent that they overlap there will be a probability that annihilation can occur. The greater the overlap, the greater the probability. "Overlap", in this context, is the integral of the product of the wavefunctions over all space.

This is the point of the answer to the question you linked; now you are asking (in essence) "what is the extent of the wave function"?

This is of course a function of the mass of the object - the uncertainty principle tells us that $$\Delta x \Delta p > \hbar$$. The better known $$p$$, the greater the uncertainty in $$x$$. Or - the lighter the particle, the larger the uncertainty in its position.

I'm not sure what uncharged particle/antiparticle pair you are thinking of...

• Hadron annihilation reaction are automatically complicated. You are likely to get some light meson and lepton pairs. Oct 22, 2015 at 0:06
• Saying that a particle is a wavefunction is very dangerous, in my opinion (although it's quite clear what you mean anyway). Oct 22, 2015 at 0:19
• Interesting! So any particle is in danger of being annihilated by its antiparticle, just with an absymally low probability. How does one compute the overlap? Integral of product of probability amplitude? Oct 22, 2015 at 6:22
• I've always thought that "isn't really a point [...] probability of finding it at any particular point" explanations are often more confusing than helpful. If they're not points, how come we still have probability of finding them at a point? And in this case: The wave functions overlapping means that it is possible that we find them at the exactly same point, right? But the probability of that would be infinitesimally small (if the particle positions are independent)? So it feels like there's still need for having positive probability of finding them close enough to each other.
– JiK
Oct 22, 2015 at 12:57
• @SurpriseDog I see - you are referring to the “sizzling cannonball”. I suppose what they are saying is that the number of contact points may be relatively small and that the energy released may suspend the cannon ball in the way that a drop of water can “float” on a hot surface. I worry about the mass of air annihilating per second by hitting your object, and how hot that would make it. Spitballing: a pressure of 1 atm means about 10 N / $\rm{cm^2}$. If average air molecules travel at 500 m/s, that means the mass of air hitting one square cm is 20 gram. All of which would annihilate. NOT SAFE. Nov 12, 2019 at 3:35