Classical Isotope Effect in Vibrational Relaxation: The Relaxation of H2 and D2

A general classical analysis of the effect of uniform mass scaling on vibrational relaxation is given which shows that the thermal rate of excitation of a system from an initially vibrationless state varies inversely as the square root of the mass ratio. This accurate classical result affords an unambiguous comparison of the augmented classical methods used by Parker and others with measurements of relaxation in H₂ and D₂. The Parker formulation of the relaxation time alone does not produce the observed isotope effect, but close agreement does result when this method is symmetrized. Consideration of the high‐temperature behavior of the ratio ${\tau }_{\mathrm{D}2}{\mathrm{\hspace{0.17em}/\hspace{0.17em}\tau }}_{\mathrm{H}2}$ shows that the deviations from the Landau‐Teller temperature dependence found by Kiefer and Lutz are simply a property of the normal relaxation process, and not a consequence of relaxation‐dissociation coupling.