The feasible applications of a new positron spectroscopy technique based on measuring of the time oscillation under positronium annihilation is analyzed.
In connection with previously revealed disagreement of theoretically calculated and measured orthopositronium decay rate in vacuum we suggest the experiment to clarify which of the positronium annihilation amplitudes R_{m},m = 0,±1 causes this disagreement. The developed for this purpose experimental procedure can also be used as the basis for the new area of positron spectroscopy, connected with the investigation of the anisotropic (spin dependent) interaction of positronium in the media.
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