Coupled Rotational-Vibrational Relaxation of Molecular Hydrogen at High Temperatures

The internal energy relaxation processes of molecular hydrogen in the temperature range of 1000-50,000 K are investigated by integrating the master equation considering all of the rotational and the vibrational energy levels simultaneously. The state-to-state and the state-specific dissociation rate coefficients used in the calculation are determined by a quasi-classical-trajectory analysis. The obtained rates are validated against the existing experimental data. Recombination rate coefficients for bulk gas are also calculated from the detailed rates and compared with the existing studies. From the calculated evolutions of energies in the rotational and the vibrational modes, the relaxation times of these two modes for the Landau-Teller equation are derived. The obtained relaxation times agree fairly well with the existing experimental data for the temperatures up to 1000 K for the rotational relaxation and up to 3000 K for the vibrational relaxation. It was revealed that these two energy modes are strongly coupled at high temperatures. The effective collision numbers required for equilibration of the two modes are found to vary from 6 to 600. The approximate expressions describing energy relaxation of the coupled ro-vibrational mode are derived for temperatures from 5000 to 50,000 K.