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The hyperfine constants A and B for magnetic dipole and electric quadrupole interaction in the 54 ground state of unstable ' Eu+ ions have been determined with high precision in an optical microwave doubleresonance experiment. The ions were produced by nuclear reactions at the ISOLDE facility at CERN, collected on a foil, reevaporated, and stored in a Paul ion trap. Three of eight possible hyperfine transitions between different F sublevels have been observed with well resolved Zeeman substructure in a residual magnetic field. Analysis of the transition frequencies and extensive second-order hyperfine correction yield values of A =559 010 325(40) Hz, 8= -926.2(3.0) kHz. A preliminary value for the nuclear quadrupole moment Q Eu+) = 1.264(23) b has also been obtained.PACS number(s): 32.30.Bv, 32.80.Pj