Cross-correlation functions for angular momentum and orientation

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Abstract
A general expression is derived that relates the generalized second moment of a rotational spectral band to an angular momentum−orientation time−correlation function for the ensemble of molecules. It is demonstrated that previous equations relating these spectral transforms to angular momentum correlation functions are recovered in the limit of short times. The extended diffusion models proposed by Gordon are used to calculate cross−correlation functions as a function of time, and the results are compared with several approximations, including the decoupling assumption widely used in spin−rotation relaxation. The cross correlations that appear in the spin−rotation problem are considered in detail. In contrast to the behavior of the spectral transform cross−correlation functions, it is explicitly demonstrated that the spin−rotation correlations for the extended diffusion models vanish after one collision.