The \gamma -decay in the quasi-continuum is used as a probe of nuclear structure properties in thermally excited nuclei. The experimental analysis is performed on high-statistics EUROBALL data on ¹⁶³Er, and the results are compared to band mixing calculations for this nucleus. Two topics are investigated. First, a direct experimental measurement of the rotational and compound damping width ({\Gamma }_rot and {\Gamma }_\mu ) is given. From a line-shape analysis of \gamma -\gamma coincidence spectra values of 200 and 20 keV are obtained for {\Gamma }_rot and {\Gamma }_\mu , respectively, in the spin region I\approx 30-40 \hbar, in good agreement with theory. Secondly, the validity of the selection rules associated with the K-quantum number are investigated as a function of the internal energy U above yrast. K-selection rules are found to be obeyed in the decay along discrete unresolved rotational bands up to U \approx 1.2 MeV, while in the interval U \approx 1.2-2.5 MeV, where the order-to-chaos transition is expected to take place, selection rules are found to be only partially valid.

PACS numbers: 21.10.Pc, 21.10.Re, 21.60.Ev, 21.60.Ka