  We present a new efficient method to compute Uehling-Uhlenbeck collision
integral for all two-particle interactions in relativistic plasma with drastic
improvement in computation time with respect to existing methods. Plasma is
assumed isotropic in momentum space. The set of reactions consists of: Moeller
and Bhabha scattering, Compton scattering, two-photon pair annihilation, and
two-photon pair production, which are described by QED matrix elements. In our
method exact energy and particle number conservation laws are satisfied.
Reaction rates are compared, where possible, with the corresponding analytical
expressions and convergence of numerical rates is demonstrated.
