  Predictions of the spectroscopic properties of low-lying states are critical
for nuclear structure studies, but are problematic for nuclei with an odd
nucleon due to the interplay of the unpaired single particle with nuclear
collective degrees of freedom. In this work, a microscopic core-quasiparticle
coupling (CQC) model based on the covariant density functional theory is
developed that contains the collective excitations of even-mass cores and
spherical single-particle states of the odd nucleon as calculated from a
quadrupole collective Hamiltonian combined with a constrained triaxial
relativistic Hartree-Bogoliubov model. Predictions of the new model for
excitation energies, kinematic and dynamic moments of inertia, and transition
rates are shown to be in good agreement with results of low-lying spectroscopy
measurements of the axially deformed odd-proton nucleus $^{159}$Tb and the
odd-neutron nucleus $^{157}$Gd. Future studies with additional nuclei are
planned.
