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.

State-by-state cross sections for dissociative electron attachment and electron-impact dissociation for molecular oxygen are computed using ab initio resonance curves calculated with the $R$-matrix method. When ${\mathrm{O}}_2$ is in its vibrational ground state, the main contribution for both processes comes from the ${}^2{\Pi }_u$ resonance state of ${\mathrm{O}}_2^{-}$ but with a significant contribution from the ${}^4{\Sigma }_u^{-}$ resonant state. Vibrational excitation leads to an increased contribution from the low-lying ${}^2{\Pi }_g$ resonance, greatly increased cross sections for both processes, and the threshold moving to lower energies. These results provide important input for models of ${\mathrm{O}}_2$-containing plasmas in nonequilibrium conditions.

Resonant vibrational excitation cross sections and the corresponding rate coefficients for electron–N₂ collisions occurring through the resonant state are reviewed. New calculations are performed using accurate potential energy curves for the N₂ electronic ground state, taken from the literature, and for the resonant state, obtained from R-matrix calculations. The calculations are extended to resonant excitation processes involving the N₂ ground state vibrational continuum, leading to dissociation. Electron-impact dissociation is found to be significant from higher vibrational levels. Accurate analytical fits for the complete set of the rate coefficients are provided. The behavior of the dissociative cross sections is investigated for rotationally excited N₂ molecules, with J = 50, 100 and 150, and for different vibrational levels.

We estimate final state interactions in the $B$-meson decays into two light vector mesons by the Regge model. We consider Pomeron exchange and charmed Regge trajectories that can relate intermediate charmed particles to the final state. The Regge poles have various helicity-flip residues, which allows a change from the longitudinal to transverse polarization. In this way a significant reduction of the longitudinal polarization fraction can be produced. In the factorization approximation we find agreement with recent data from the BABAR and Belle Collaborations in the $B\to K^{*}\varphi$ decay channel, as a result of an appropriate choice of semileptonic form factors and Regge exchanges. On the other hand, data for the $K^{*}\rho$ decay channels appear more elusive. The soft effects discussed in the present paper are based on a model of Regge trajectories that is shown to reproduce correctly in the noncharmed case the Regge phenomenology of light mesons.

Electron energy distribution functions have been calculated by a self-consistent model which couples the electron Boltzmann equation with vibrationally and electronically excited state kinetics and plasma chemistry. Moderate pressure nitrogen gas discharges in the E/N range from 30 to 60 Townsend are investigated comparing an electron-impact cross section set considering transitions starting from all the vibrational states, with reduced models, taking into account only collisions involving the ground vibrational level. The results, while confirming the important role of second kind collisions in affecting the eedf, show a large dependence of the eedf on the set of inelastic processes involving vibrationally and electronically excited molecules, pointing out the need of using a cross section database including processes linking excited states in non-equilibrium plasma discharge models.