Rotational relaxation in molecular hydrogen and deuterium: theory versus acoustic experiments

An explicit formulation of the rotational relaxation time in terms of state-to-state rate coefficients associated to inelastic collisions is reported. The state-to-state rates needed for the detailed interpretation of relaxation in H2 and D2, including isotopic variant mixtures, have been calculated by solving the close-coupling Schrödinger equations using the H2-H2 potential energy surface by Diep and Johnson [J. Chem. Phys. 112, 4465 (2000)]. Relaxation related quantities (rotational effective cross section, bulk viscosity, relaxation time, and collision number) calculated from first principles agree reasonably well with acoustic absorption experimental data on H2 and D2 between 30 and 293 K. This result confirms at once the proposed formulation, and the validation of the H2-H2 potential energy surface employed, since no approximations have been introduced in the dynamics. Accordingly, the state-to-state rates derived from Diep and Johnson potential energy surface appear to be overestimated by up to 10% for H2, and up to 30% for D2 at T = 300 K, showing a better agreement at lower temperatures.