  The hyperfine splitting of the 5g -> 4f transitions in muonic 185,187-Re has
been measured using high resolution HPGe detectors and compared to
state-of-the-art atomic theoretical predictions. The spectroscopic quadrupole
moment has been extracted using modern fitting procedures and compared to the
values 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 of
a larger effort at the Paul Scherrer Institut towards the measurement of the
nuclear charge radii of radioactive elements.
