Studying inelastic collisions of H$_{2}$ and D$_{2}$ by means of ultrasonic experiments*

An explicit formulation for the rotation-translation relaxation time in terms of state-to-state rate coefficients associated to inelastic collisions is presented. The formulation provides a tangible link between acoustic and gas dynamics, and quantum scattering calculations. The state-to-state rates needed for the detailed interpretation of relaxation of H$_{2}$ and D$_{2}$, including isotopic variant mixtures, have been calculated by solving the close-coupled Schr{\"o}dinger equations. Relaxation related quantities (rotational cross section, bulk viscosity, relaxation time, and collision number) calculated from first principles agree reasonably well with acoustic absorption experimental data on H$_{2}$ and D$_{2}$ well below 293 K. This result confirms the proposed formulation, the quantum scattering calculations, and the potential energy surface employed.