Vibrational energy relaxation in liquid oxygen (revisited) and in liquid nitrogen

The lifetimes of the first excited vibrational states in liquid oxygen and nitrogen are very long: 2.5 ms and 56 s, respectively. The theoretical calculation of these long lifetimes is challenging, ultimately because in each case the vibrational energy gap is much higher both than $\mathrm{kT}$ and than characteristic translational and rotational frequencies of the molecules in the liquid. A few years ago we presented a theoretical calculation for the vibrational lifetime in liquid oxygen based on a semiclassical implementation of Fermi’s golden rule. In this paper we improve upon that work, primarily by using an improved intermolecular potential, and what we believe is a more reliable quantum correction factor. Our theoretical result for the lifetime at 77 K is in reasonable agreement with experiment. We also present a calculation for liquid nitrogen at 77 K. In this case our result for the (nonradiative) lifetime is about a factor of 35 longer than the experimental lifetime, lending support to the belief that in liquid nitrogen the vibrational lifetime is in fact radiative.