The modeling of atmospheric gas, interacting with the space vehicles in re-entry conditions in planetary exploration missions, requires a large set of scattering data for all those elementary processes occurring in the system. A fundamental aspect of re-entry problems is represented by the strong non-equilibrium conditions met in the atmospheric plasma close to the surface of the thermal shield, where numerous interconnected relaxation processes determine the evolution of the gaseous system towards equilibrium conditions. A central role is played by the vibrational exchanges of energy, so that collisional processes involving vibrationally excited molecules assume a particular importance. In the present paper, theoretical calculations of complete sets of vibrationally state-resolved cross sections and rate coefficients are reviewed, focusing on the relevant classes of collisional processes: resonant and non-resonant electron-impact excitation of molecules, atom–diatom and molecule–molecule collisions as well as gas-surface interaction. In particular, collisional processes involving atomic and molecular species, relevant to Earth (N ₂ , O ₂ , NO), Mars (CO ₂ , CO, N ₂ ) and Jupiter (H ₂ , He) atmospheres are considered.

Electron-impact theoretical cross sections and rate coefficients for vibrational excitation of vibrationally excited H${}_{2}$ molecules, occurring through the H${}_{2}^{$-${}}$ resonant species in the ${}^{2}{$\Sigma${}}_{g}^{+}$ Rydberg-excited electronic state, are presented. The cross sections are calculated as functions of the incident electron energy by adopting the local-complex-potential model for resonant collisions and by using ab initio calculated molecular potentials and resonance widths. The calculations have been extended to all possible vibrational transitions linking all 15 vibrational levels of the electronic ground state of the H${}_{2}$ molecule. The corresponding rate coefficients are also obtained as a function of the electron temperature by assuming a Maxwellian electron energy distribution function, and a simple analytical expression is derived. Finally, the present rate coefficients for the transitions starting from the lowest vibrational level of the H${}_{2}$ molecule are compared with those for the process involving the ${X}^{2}{$\Sigma${}}_{u}^{+}$ resonant state of the H${}_{2}^{$-${}}$ molecular ion.

We report cross-sections and rate coefficients for excited states colliding with electrons, heavy particles and walls useful for the description of H ${}_2$ /He plasma kinetics under different conditions. In particular, the role of the rotational states in resonant vibrational excitations of the H ${}_2$ molecule by electron impact and the calculation of the related cross-sections are illustrated. The theoretical determination of the cross-section for the rovibrational energy exchange and dissociation of H ${}_2$ molecule, induced by He atom impact, by using the quasi-classical trajectory method is discussed. Recombination probabilities of H atoms on tungsten and graphite, relevant for the determination of the nascent vibrational distribution, are also presented. An example of a state-to-state plasma kinetic model for the description of shock waves operating in H ${}_2$ and He-H ${}_2$ mixtures is presented, emphasizing also the role of electronically-excited states in affecting the electron energy distribution function of free electrons. Finally, the thermodynamic properties and the electrical conductivity of non-ideal, high-density hydrogen plasma are finally discussed, in particular focusing on the pressure ionization phenomenon in high-pressure high-temperature plasmas.

Electron-impact cross sections for the dissociation process of vibrationally excited He molecular ion, as a function of the incident electron energy are calculated for the dissociative transition by using the R-matrix method in the adiabatic-nuclei approximation. The potential energy curves for the involved electronic states and transition dipole moment, also calculated with the R-matrix method, were found to be in good agreement with the results reported in literature. The vibrationally resolved dissociation cross sections of He exhibit a resonant structure around 7 eV. The observed strong variation of the magnitude of this structure with the vibrational level is explained in terms of the overlap of initial and final (continuum) state wave functions in the Franck–Condon region.