Direct Measurement of Rotational Relaxation
Authors: Unland M. L. , Flygare W. H. 
Published: January 2005

Several types of microwave double-resonance experiments are performed using a double-bridge superheterodyne detection scheme. The first set of experiments clarify some features of the double quantum effect and also confirm earlier experiments in a Stark-modulated spectrometer.
The second set of experiments employs the double-bridge technique and the wide bandwidth capability of the 30-Mc/sec amplifiers to measure directly the restoration to equilibrium of a nonequilibrium system. Nonequilibrium conditions are produced in the OCS J=0, 1, and 2 rotational energy levels by applying high microwave power resonant with the J=0→1 transition and simultaneously observing the J=1→2 transition. The intensity of the J=1→2 transition was found to relax to equilibrium with a first-order exponential dependence by direct observation of the amplitude of the 30-Mc/sec carrier as a function of time after the signal irradiating the J=0→1 transition was cut off. The direct method of measuring rotational relaxation was carried out as a function of pressure. The linewidths were also measured in a steady-state experiment in the same apparatus and the relaxation results are compared to the above direct method of observation. The direct method leads to relaxation times half as long as the relaxation times obtained from the corrected linewidth data (τeff=8.43 μsec·μ, τ=17.51 μsec·μ). This factor of 2 is explained by consideration of the basic difference between the two types of measurements.
The relaxation times of OCS in 1:1 ratios with Ar, He, and O2 were also measured by the direct method. In these cases the relaxation times lead to collision diameters of dOCS—OCS=10.2 Å, dOCS—Ar=8.3 Å, dOCS—He=5.5 Å, and dOCS—O2=6.3 Å. The phenomena of the nonmixing of the J=1, m=0, and m=±1 states upon irradiation of the J=0→1, m=0→0 transition is investigated in the pure OCS and mixed OCS—O2 cases. No mixing was observed in either case. A plausible explanation is offered based on the second-order Stark effect and the first-order Zeeman effect, both of which are present during a collision.
Several methods of improving on the signal-to-noise ratio obtained in the direct method of observing rotational relaxation times are pursued with the interest being the extension to the measurement of vibrational relaxation. We have shown the feasibility of periodically repeating the above direct-measurement experiment (at a time slower than the relaxation time) and observing the relaxation time as a phase shift due to the delayed response of the population in the molecular energy levels. In another experiment we have shown the feasibility of extracting the X-band (J=0→1) modulation frequency from the 30-Mc/sec carrier to obtain an amplitude depending only on the modulation efficiency or population modulation of the J=1→2 transition. By studying the amplitude of the modulation frequency as a function of modulation frequency, one can again extract relaxation information. Both of these latter methods could be applied in a Stark-modulated spectrometer.
The future of relaxation experiments using microwave spectroscopy appears to be in the areas of observing transient species, in gaseous chemical kinetics, and studies of lifetimes of excited vibrational states in molecules.