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 dissociation reaction in N2 molecules. For VV- and VT-transitions the original approximations of the rate coefficients have been modified to make it possible application of the inverse Laplace transformation in the analytical form. A satisfactory approximation of the state-to-state dissociation rate coefficient allowing for the application of the inverse Laplace transformation is also proposed. For all 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 cross sections of VV transitions increase almost linearly with the energy of colliding particles. VT-exchanges and dissociation reaction manifest threshold behaviour, and their cross sections are non-monotonic. Dissociation threshold is considerably shifted towards 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 non-equilibrium fluid dynamics while simulating rarefied gas flows using the direct Monte-Carlo methods. Refs 23. Figs 4. Tables 2.