Protokernel of the inverse collision integral of the Boltzmann equation for an isotropic scattering cross section

It is shown that any kernel of the collision integral of the nonlinear Boltzmann equation isotropic in velocities can be expressed in terms of a universal protokernel independent of the model of interaction between particles by single integration with the interaction cross section. This makes it possible to calculate any kernels of an anisotropic Boltzmann equation and use for their constructing the recurrent relations obtained earlier at the protokernel level. We consider three different expressions for the protokernel, including that for an arbitrary ratio of the masses of colliding particles.