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 ?
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.
When one is in the micro level of particles one has to stop thinking classically, i.e. with terms we have developed from our macroscopic observations.
"Touch" at the particle level can be defined as "interaction". Our feeling of touch actually does involve the electromagnetic interactions, we touch with the field of the molecules in our hand the field of the other objects, and this touching involves the exchange of force carrying virtual particles, i.e. particles which do not have definite mass but retain their quantum numbers characterizing them.
There is a precise mathematical description given graphically by the Feynman diagrams:
The diagram translates one to one with integrals that give the probability of this interaction happening. The exchanged electron in this diagram( or positron, depending on how one reads this) is virtual, it does not have definite mass.
Then the closer the e+ and e- are to each other the larger the probability that the scattering will result to an annihilation. So annihilation happens according to the probability of interaction.There are higher order exchanges but they give much smaller probabilities.
