Inverse Laplace transform as a tool for calculation of state-specific cross sections of inelastic collisions

Abstract

In the present work we study the cross sections of VV (vibration-vibration), VT (vibration-translation) energy exchanges and state-specific dissociation reactions in N2 and O2 molecules. Applying the inverse Laplace transform to approximations for state-resolved rate coefficients obtained by quasi-classical trajectory calculations we derive analytical expressions for the cross sections. The results are analyzed in a wide range of energies and vibrational levels. It is shown that cross sections of VV transitions increase almost linearly with the energy of the colliding particles. VT exchanges and dissociation reactions manifest threshold behaviour, and their cross sections are non-monotonic. The dissociation threshold is considerably shifted 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 non-equilibrium fluid dynamics while simulating rarefied gas flows using DSMC methods.