  A new technique of elucidating $\beta$-decay schemes of isotopes with large
density of states at low excitation energies has been developed, in which a
Broad Energy Germanium (BEGe) detector is used in conjunction with coaxial
hyper-pure germanium detectors. The power of this technique has been
demonstrated on the example of 183Hg decay. Mass-separated samples of 183Hg
were produced by a deposition of the low-energy radioactive-ion beam delivered
by the ISOLDE facility at CERN. The excellent energy resolution of the BEGe
detector allowed $\gamma$ rays energies to be determined with a precision of a
few tens of electronvolts, which was sufficient for the analysis of the
Rydberg-Ritz combinations in the level scheme. The timestamped structure of the
data was used for unambiguous separation of $\gamma$ rays arising from the
decay of 183Hg from those due to the daughter decays.
