Inverse Laplace transformation for evaluation of state-specific cross sections for dissociation reaction and vibrational energy transitions

Abstract

In the present work, we study the cross sections of VV (vibration-vibration) and VT (vibration-translation) energy exchanges in nitrogen and oxygen, as well as the vibrational state-specific cross sections of the dissociation reaction in N₂ molecules. For VV- and VT-transitions the original approximations of the rate coefficients have been modified to make it possible to apply the inverse Laplace transformation in the analytical form. A satisfactory approximation of the state-resolved dissociation rate coefficient allowing for the application of the inverse Laplace transformation is also proposed. For all the considered reactions, analytical expressions for the cross sections are obtained. The results are analyzed in the wide range of energies and vibrational levels. It is shown that the cross sections of VV transitions increase almost linearly with the energy of the colliding particles. VT-exchanges and the dissociation reaction manifest threshold behavior and their cross sections are nonmonotonic. The dissociation threshold shifts significantly towards the low-energy region for high vibrational states. Using the hard sphere model for the dissociation cross section results in significant inaccuracy. The results of our work can be applied in nonequilibrium fluid dynamics, while simulating rarefied gas flows using the direct Monte-Carlo methods.