  The nuclide $^{176}$Lu is one of the few naturally occurring isotopes that
are potentially unstable with respect to electron capture (EC). Although
experimental evidence for $^{176}$Lu EC decay is still missing, this isotope is
instead well known to $\beta^-$ decay into $^{176}$Hf with an half-life of
about 38 Gyr. The precise investigation of all $^{176}$Lu possible decay modes
is interesting because the Lu/Hf ratio is adopted as an isotopic clock.
Previous searches for the $^{176}$Lu EC decay were performed by using a passive
Lutetium source coupled with an HP-Ge spectrometer. Our approach uses a LYSO
crystal both as Lutetium source and as an active detector. Scintillation light
from the LYSO crystal is acquired in coincidence with the signals from the
HP-Ge detector, this allows a powerful suppression of the background sourcing
from the well known $\beta^-$ decay branch. This coincidence approach led to an
improvement on the $^{176}$Lu EC branching ratio limits by a factor 3 to 30,
depending on the considered EC channel.
