The quantum impulse approximation theory has been extended to the inelastic collision. The total inelastic cross sections for the degenerated states with different angular momenta was calculated. It was proved that summing over the transitions from nl to n' andfrom nl to n'l' would give us the total cross section of transition from n to n'. Rate coefficients were calculated for the common gases in the atmosphere being the third particle. The resonant effect of the rate coefficients had been observed. Recombination coefficients were then calculated in terms of rate coefficients. Previous calculations were carried out in compare with the net rate flow through certain excited levels, which were found to be more stable and reflected a clearer picture of the whole process. Results have been compared with the elastic collision. A dramatic decreasing of rates when temperature increased was also observed. More thermal energy increases the probability of electrons for being re-ionized. Similar calculations had been carried out for the upper atmosphere gases, such as N₂, O₂, CO, CO₂, and H₂O. The recombination coefficients for electron combining with metallic ion Na+ were also calculated.
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