  The validity of the K-quantum number in rapidly rotating warm nuclei is
investigated as a function of thermal excitation energy U and angular momentum
I, for the rare-earth nucleus 163Er. The quantal eigenstates are described with
a shell model which combines a cranked Nilsson mean-field and a residual
two-body interaction, together with a term which takes into account the angular
momentum carried by the K-quantum number in an approximate way. K-mixing is
produced by the interplay of the Coriolis interaction and the residual
interaction; it is weak in the region of the discrete rotational bands (U
\lesim 1MeV), but it gradually increases until the limit of complete violation
of the K-quantum number is approached around U \sim 2 - 2.5 MeV. The calculated
matrix elements between bands having different K-quantum numbers decrease
exponentially as a function of $\Delta K$, in qualitative agreement with recent
data.
