Collision between Two Particles

Abstract

In the first chapter we briefly considered a collision between two particles A and B and obtained a relationship between the differential cross sections in the center-of-mass frame and in the laboratory frame. However, to obtain the scattering amplitude we have to know the nature of the interaction between the two particles. In this chapter we obtain the scattering amplitudes for collisions between an incident particle A and a target B under the following different conditions: (1) A and B are distinguishable from each other. (2) A and B are identical but follow classical mechanics; hence, they can be distinguished by their trajectories. (3) A and B are identical and are either bosons (follow Bose-Einstien statistics) or fermions (follow Fermi-Dirac statistics). For the bosons, the total wave function (including spins) of the system is symmetric, i.e., the wave function is unchanged on the exchange of A and B. On the other hand, for the fermions, the total wave function is antisymmetric and changes its sign on the exchange of A and B.