### 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 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., T_{1} or T_{2}) 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-, O_{2}-, N_{2}-rare gas systems.

Original language | English (US) |
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Pages (from-to) | 1981-1987 |

Number of pages | 7 |

Journal | The Journal of chemical physics |

Volume | 68 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1977 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry