PLEASE HELP. VB particle sim. Rate of neutrilization of charge

[jibrownie]

I'm making a basic charged particle sim in vb, and need to know the rate at which a charge will neutrilize if it comes in contact with a particle with an opposite charge, assuming both particles are perfectly cylindrical and of infanitesimal size.

 

[Bob S]

The most infinitesimal (smallest) point charges I know are the electron and positron. They get captured in the positronium atomic orbitals with high (n,l), and cascade down to the 1s atomic state before annihilating (mutual neutralization). The lifetime of positronium in the ³S₁ state is about 140 nanoseconds, and 125 picoseconds in the ¹S₀ state.
However, if a proton stops in a solid, it very quickly captures an electron in a high orbital (n,l) state (estimates are about 10^-12 sec), but it takes a long time to cascade down to the 1s state. The lifetime of the 6h state is 610 nanoseconds, and 1.6 nanoseconds for the 2p state. So for charged ions, it really depends on the specific situation.