antimatteratomic-physicsforcesparticle-physics
It is known that matter and antimatter annihilate each other when they "touch" each other. And as far as I know, the concept of "touching" as our brain gets it is not true on the atomic level since atoms never really touch each other but only get affected by different forces.
If this is true, then when does the annihilation really happen ?
Does it happen when two atoms are affected by each others repulsion force for example ?
I believe this is where your thought experiment goes wrong: However, the nuclei are so small and so widely separated that presumably they just orbit each other as the electron clouds annihilate
Why would they be widely separated? Solids touch in order of nanometers. The protons and antiprotons would attract each other with the 1/r^2 electric field, which is very strong. Even if the energy of the projectile is small enough to form "protoniums", ie. have antiprotons in the place of electrons in the quantum mechanical solution, the wave function will be so large that the protons antiproton wave function will overlap and annihilate. The lifetime is of the order of .1 to 10 microseconds.
To get an idea of the annihilation Here is a bubble chamber photo of an antiproton entering from below annihilating on a proton at rest int he chamber. The multiplicity is on pions and kaons which will then decay with their characteristic decays.
The multiplicity is high even for annihilation at rest.
If the projectile has high enough energy, it will be a scattering with the cross section of antiproton on proton, depending on the area, to get the percentage annihilated. It is very difficult to get a plasma of protons and antiprotons anyway. Annihilations have a very large crossection. The antiprotons will either scatter elastically if they have enough energy, and leave the samples or annihilate if in the region of protons.
If the two bits of matter are in space with only their own gravity, then some will escape a first scatter and then fall back and annihilate or escape if they have escape velocity.
Here is the elementary particle table from which all others are built up , the standard model of particle physics.
Which shows the conserved quantum numbers that characterize the particles (columns and rows have quantum numbers assigned too) plus the measured masses. The quantum numbers have to "annihilate" to have an annihilation event, i.e. they should become 0 after annihilation. Mass is not a quantum number , it is a "length" in the energy momentum vector of the particles. Conservation of quantum numbers in interactions allow the mass to remain invariant. If quantum numbers are annihilated there is no constraint on the total energy momentum vector other than energy conservation, and the products allow that.
Here is a Feynman diagram of e+e- annihilation
There is no extra energy except the four vector of each incoming lepton. Charge is just a number counting attribute here.
Here is e+e- annihilation when the energies are large enough to create a muon pair
and a more complicated one into b bbar jets
In all these the quantum numbers annihilate on the left and new quantum numbers from 0 create pairs with oposite quantum numbers, according to the probabilities for the interaction at that energy.
In a nutshell: it is the quantum numbers that become annihilated/0 , freeing the energy momentum fourvectors to display their creativity :)
Best Answer
You should not think a particle as point like. Classically, the probability of two point like particles colliding with random location and velocity is 0, that is why you said it never happens.
However, at quantum mechanical level, these particle are described by wavefunction. It means that there is spreading in its spatial location, say 0.1nm (the minimum spreading is guaranteed by Heisenberg's uncertainty principle). The probability of annihilation can therefore be calculated by the overlap of these wavefunction and their interaction. This overlap is the meaning of "touching" in some sense.