  Highly-excited single-particle states in nuclei are coupled with the
excitations of a more complex character, first of all with collective
phonon-like modes of the core. In the framework of the quasiparticle-phonon
model we consider the structure of resulting complex configurations using the
$1k_{17/2}$ orbital in $^{209}$Pb as an example. Although, on the level of one-
and two-phonon admixtures, the fully chaotic GOE regime is not reached, the
eigenstates of the model carry significant degree of complexity that can be
quantified with the aid of correlational invariant entropy. With artificially
enhanced particle-core coupling, the system undergoes the doubling phase
transition with the quasiparticle strength concentrated in two repelling peaks.
This phase transition is clearly detected by correlational entropy.
