Vibrational relaxation of diatomic molecules

Numerical solution of vibrational excitation of diatomic molecules by collision with noble gas atoms is obtained using $\mathrm{O}_2$ collisions with $\mathrm{Ar}$ in temperature range $1000$ to $20,000$ K; also in classical approach analytical expression was obtained; knowing intermolecular potential, time of vibrational relaxation is deduced; results are in agreement with experiments in shock tubes.