Validation of Bohr criterion for Binary Collisions Under Debye Potential

The differential and transport cross sections for binary collision are fundamental parameters to depict the traversing of charged particles in matters, which are often obtained by classical mechanics. The Bohr criterion was proposed to judge when the treatment via classical mechanics is reliable. However, quantitative comparisons of the cross sections are very few between classical and quantum methods under Debye potential. In the work such comparisons are made for a wide ranges of collision velocity, ion charge state and Debye length. For differential cross section a quantitative range of velocity is obtained for Bohr criterion to be invalid for ion-ion collision, and the criterion is found to be almost invalid for electron-ion collision. For the transport cross section, the quantitative range of velocities is given for the criterion to be valid for both ion-ion and electron-ion collisions. The reason for the failure of classical mechanics at high velocities is explored.