On the use of various scaling theories in the deconvolution of rotational relaxation data: Application to pressure-broadened linewidth measurements

The inversion of pressure-broadened spectral linewidth data to yield state-to-state rotationally inelastic rate constants is considered. Deconvolution procedures are presented based upon the rate relationships given by the information theory (IT), infinite order sudden (IOS), and dynamic-coupling theory (DCT) formalisms. In addition, a statistical analysis for the IOS and DCT inversion methods is developed. The three scaling theories are applied to the inversion of experimental data for the CO-He, CO-Ne, HCl-He, and HCl-Ne systems. The results indicate that the IT formalism is inappropriate for deconvoluting linewidth data. For the IOS method the extreme sensitivity of the rates to uncertainties in the measurements can often make the extracted rates unreliable. The DCT inversion procedure is shown to be stable and to yield reliable rates. The application of the DCT method to simulated linewidth data for the He-HCN system yields rates in excellent agreement with ab initio calculated values and correctly predicts the propensity for even rotational changes in this near-homonuclear system. The necessary input for an inversion is the widths as a function of rotational level. We conclude that accurate linewidth measurements contain a wealth of detailed state-to-state collisional information which can now be obtained directly by use of the DCT inversion technique.