Recent progress in the spectroscopy of antiprotonic helium has allowed for measuring the separation between components of the hyperfine structure (hfs) of the (37,35) metastable states with an accuracy of 300 kHz, equivalent to a relative accuracy of 3x10(-5). The analysis of the uncertainties of the available theoretical results on the antiprotonic helium hfs shows that the accuracy of the value of the dipole magnetic moment of the antiproton (currently known to only 0.3%) may be improved by up to two orders of magnitude by measuring the splitting of appropriately selected components of the hfs of any of the known metastable states. The feasibility of the proposed measurement by means of an analog of the triple resonance method is also discussed.
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