Validation of Classical Transport Cross Section for Ion-Ion Interactions Under Repulsive Yukawa Potential

Abstract

Value of cross section is a fundamental parameter to depict the transport of charged particles in matters. Due to masses of orders of magnitude higher than electrons and convenience of realistic calculation, the cross section of elastic nuclei-nuclei collision is usually treated via classical mechanics. The famous Bohr criterion was firstly proposed to judge whether the treatment via classical mechanics is reliable or not. Later, Lindhard generalized the results of Coulomb to screening potentials. Considering the increasing importance of detailed ion-ion interactions under modern simulation codes in inertial confinement fusion (ICF) researches, the validation of classical transport cross section for ion-ion interactions in a big range of parameter space is certainly required. In this work, the transport cross sections via classical mechanics under repulsive Yukawa potential are compared with those via quantum mechanics. Differences of differential cross sections are found with respect to scattering angles and velocities. Our results generally indicate that the classical picture fails at the cases of both low and high velocities, which represent a significant extension of the famous Bohr criterion and its generalized variations. Furthermore, the precise validation zones of classical picture is also analysed in this work. This work is of significant importance for benchmarking the modern ion-kinetic simulation codes in ICF researches, concerning the stopping power of $\alpha$ particles in DT fuels, ion-ion friction and viscous effects in the formation of kinetic shocks.