Abstract
The line broadening of recoilless radiation has recently become an important tool for studying isomer shifts and nuclear magnetic-dipole and electric-quadrupole interactions with crystalline fields. When the line shape is not well resolved, it is not always possible to obtain the desired information from experimental velocity spectra. It is pointed out that the use of moment theorems can sometimes give access to quantitative information which would not otherwise be available. The results given apply only to powdered samples, and then only in the absence of any anisotropy of the recoilless radiation or absorption being analyzed.

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