  A new form of the model collision operator for a Boltzmann gas of hard
spheres and Coulomb plasma is derived. One-component and many-component systems
are considered. The collision operator proposed takes properly into account the
relaxation of the first 13 hydrodynamic moments. An expression for the
intensity of the Langevin source in the model kinetic equation is obtained in
the same approximation. A technique for reconstruction of the model collision
integral based on a known expression for the model linearized operator is
proposed. It is shown that, within our model, the collision integral does not
contain a complicated exponential, common for the ellipsoidal statistical type
models. Boltzmann's H-theorem is proved for our model.
