Scaling theoretic deconvolution of bulk relaxation data: State-to-state rates from pressure-broadened linewidths

Inversion of certain types of relaxation data is shown to be possible by application of two new developments. First, a recently developed scaling theory of rotationally inelastic cross sections is utilized in deriving the corresponding formulas for the state-to-state rate constants k _jj′. Second, practical means are presented for assessing the number of independent pieces of information contained in the experimental data. Application of this work to simple relaxation times (i.e., T₁ or T₂) provides an essential reduction in the number of unknowns and allows for the determination of the rates k_0Δ by inversion of a set of algebraic equations subject to the constraints k_0Δ≥ 0. The dimensionality of this set of equations is related to the number of independent pieces of information contained in the experimental data. A stable and fast method for solving the equations is given. The inversion of pressure broadening data to yield state-to-state rate constants is illustrated for the CO-, O₂-, N₂-rare gas systems.