Integration of the Boltzmann collision term over scattering angles

Abstract

In case the distribution function of the field particle is Maxwellian, the Boltzmann collision term for both Coulomb and smooth rigid elastic interaction is directly integrated over scattering angles without using Taylor series expansion. For Coulomb interaction, a cutoff of Δvα min is introduced instead of the usual θmin cutoff. A Boltzmann collision term of the form (∂fα/∂t)c=∫[G(v′α) −G(vα)]C(vα,v′α)dv′α is obtained.