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The hyperfine splitting of the 5g -> 4f transitions in muonic 185,187-Re hasbeen measured using high resolution HPGe detectors and compared tostate-of-the-art atomic theoretical predictions. The spectroscopic quadrupolemoment has been extracted using modern fitting procedures and compared to thevalues available in literature obtained from muonic X rays of natural rhenium.The extracted values of the nuclear spectroscopic quadrupole moment are 2.07(5)barn and 1.94(5) barn, respectively for 185-Re and 187-Re. This work is part ofa larger effort at the Paul Scherrer Institut towards the measurement of thenuclear charge radii of radioactive elements.

The measurement of the quadrupole moment of 185-Re and 187-Re from the hyperfine structure of muonic X rays