Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei

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.