A Note on Saturation in Microwave Spectroscopy

The investigation of Van Vleck and Weisskopf, on the shape of collision-broadened absorption lines, is extended to high power levels of the exciting radiation. Transitions among the molecular states are then induced at a rate that is not negligible compared with the collision rate, thus invalidating the assumption of thermal equilibrium. The theory is based on a quantum transcription of the previous semiclassical treatment, the essential tool being the density matrix. When the resonant frequencies of the molecule are widely spaced, an absorption line is ultimately broadened as the power level increases. Correspondingly, the peak absorption coefficient decreases, the power absorbed per unit volume approaching saturation with increasing incident power. It is shown that the broadening of an absorption line is not to be attributed to any intrinsic modification of the line shape, but rather to a frequency dependent alteration of the energy level populations. A molecule for which all resonant frequencies coincide, a one-dimensional harmonic oscillator, is treated in Appendix II. No saturation effect occurs here, since the absorption is independent of the molecular distribution among the oscillator energy levels.