Head-On Collisions of True Point Charges

[what_are_electrons]

Since the electron and the positron are indeed true "point charges" then why are the colliders able to make them collide head-on?

 

[zefram_c]

As free particles, the electron and positron are not localized; they are represented by wave packets that have finite spatial extent. Furthermore, it is not necessary for them to collide *precisely* head-on for something interesting to happen. Consider the hydrongen-like 'atom' where the proton is replaced by a positron. This system is called positronium, and has been extensively studied. It decays by self-annihilation into photons, but the wavefunctions describing the system are those of a hydrogen atom.

 

[humanino]

The particles interact via another exhanged virtual particle, which is called a vector boson. For instance, the vector boson for electromagnetic interaction is the photon. Classically thinking, one would say that one particle is actually scattered by the field created around the other particle. Now, the shape of this field depends on the distribution of the charges : for pointlike particles, the distribution is called a "Dirac peak". If the electron were a small ball, as for instance is the proton, then the distribution would look like a fuzzy sphere, as it actually does for the proton, but does not (as precisely as we can see) for the electron.

To be more accurate, the potential for the field created by a distribution of charge is given by the Fourier transform of the distribution (in a certain approximation).