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

Abstract

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 kjj′. 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 k0Δ by inversion of a set of algebraic equations subject to the constraints k0Δ?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.